The biblical foundation for the idea of the evangelical counsels is found in such texts as 1 Corinthians 7 and Matthew 19:10-12. In the latter text, Jesus has just taught his disciples that divorce is unlawful. The disciples are quite surprised at this teaching:
His disciples said to him, “If such is the case of a man with his wife, it is better not to marry.” But he said to them, “Not everyone can accept this teaching, but only those to whom it is given. For there are eunuchs who have been so from birth, and there are eunuchs who have been made eunuchs by others, and there are eunuchs who have made themselves eunuchs for the sake of the kingdom of heaven. Let anyone accept this who can.”
In 1 Corinthians 7, Paul is giving commands and advice (counsel!) to the Corinthians regarding matters connected to marriage:
Now concerning the matters about which you wrote: “It is well for a man not to touch a woman.” But because of cases of sexual immorality, each man should have his own wife and each woman her own husband. The husband should give to his wife her conjugal rights, and likewise the wife to her husband. For the wife does not have authority over her own body, but the husband does; likewise the husband does not have authority over his own body, but the wife does. Do not deprive one another except perhaps by agreement for a set time, to devote yourselves to prayer, and then come together again, so that Satan may not tempt you because of your lack of self-control. This I say by way of concession, not of command. I wish that all were as I myself am. But each has a particular gift from God, one having one kind and another a different kind.
To the unmarried and the widows I say that it is well for them to remain unmarried as I am. But if they are not practicing self-control, they should marry. For it is better to marry than to be aflame with passion. . . .
However that may be, let each of you lead the life that the Lord has assigned, to which God called you. This is my rule in all the churches. . . . In whatever condition you were called, brothers and sisters, there remain with God.
Now concerning virgins, I have no command of the Lord, but I give my opinion as one who by the Lord’s mercy is trustworthy. I think that, in view of the impending crisis, it is well for you to remain as you are. Are you bound to a wife? Do not seek to be free. Are you free from a wife? Do not seek a wife. But if you marry, you do not sin, and if a virgin marries, she does not sin. Yet those who marry will experience distress in this life, and I would spare you that. I mean, brothers and sisters, the appointed time has grown short; from now on, let even those who have wives be as though they had none, and those who mourn as though they were not mourning, and those who rejoice as though they were not rejoicing, and those who buy as though they had no possessions, and those who deal with the world as though they had no dealings with it. For the present form of this world is passing away.
I want you to be free from anxieties. The unmarried man is anxious about the affairs of the Lord, how to please the Lord; but the married man is anxious about the affairs of the world, how to please his wife, and his interests are divided. And the unmarried woman and the virgin are anxious about the affairs of the Lord, so that they may be holy in body and spirit; but the married woman is anxious about the affairs of the world, how to please her husband. I say this for your own benefit, not to put any restraint upon you, but to promote good order and unhindered devotion to the Lord.
If anyone thinks that he is not behaving properly toward his fiancée [Gk. virgin], if his passions are strong, and so it has to be, let him marry as he wishes; it is no sin. Let them marry. But if someone stands firm in his resolve, being under no necessity but having his own desire under control, and has determined in his own mind to keep her as his fiancée, he will do well. So then, he who marries his fiancée does well; and he who refrains from marriage will do better.
A wife is bound as long as her husband lives. But if the husband dies, she is free to marry anyone she wishes, only in the Lord. But in my judgment she is more blessed if she remains as she is. And I think that I too have the Spirit of God.
The Catechism of the Catholic Church deals with the evangelical counsels especially here (1973-1974 and here (914-933):
1973 Besides its precepts, the New Law also includes the evangelical counsels. The traditional distinction between God's commandments and the evangelical counsels is drawn in relation to charity, the perfection of Christian life. The precepts are intended to remove whatever is incompatible with charity. The aim of the counsels is to remove whatever might hinder the development of charity, even if it is not contrary to it.
1974 The evangelical counsels manifest the living fullness of charity, which is never satisfied with not giving more. They attest its vitality and call forth our spiritual readiness. The perfection of the New Law consists essentially in the precepts of love of God and neighbor. The counsels point out the more direct ways, the readier means, and are to be practiced in keeping with the vocation of each:
The Catechism here (in 1974) adds a relevant quotation from St. Francis de Sales:
[God] does not want each person to keep all the counsels, but only those appropriate to the diversity of persons, times, opportunities, and strengths, as charity requires; for it is charity, as queen of all virtues, all commandments, all counsels, and, in short, of all laws and all Christian actions that gives to all of them their rank, order, time, and value. (Footnotes removed here and above)
Here is my articulation, in my own words, of the basic idea:
The ultimate goal of our lives is the beatific vision, where we will enjoy God fully forever. In this life, we are all called to live lives of charity--of supreme love to God, and love to our neighbors for God's sake. The commandments of God lay out the specifics of how we are all called to live in the love of God. Beyond the commandments of God's law are the evangelical counsels. The counsels lay out a way to live a life especially and particularly devoted to God and to God's service. There is the counsel of poverty, which calls individuals to abandon personal ownership of worldly possessions. There is the counsel of chastity, which invites to the renunciation of married life. And there is the counsel of obedience, in which we are invited to put ourselves in a special way under the authority and guidance of spiritual or ecclesiastical guides (such as by committing to a religious order).
Since the evangelical counsels portray a life which is lived in full, direct service to God and with a fuller focus on God than one would experience in other life callings, it can be said that, in a sense, the way of life proposed by the counsels is better than other forms of living. The more we are able to live a life focused on God and in his direct service, the better, all other things being equal. St. Paul alludes to this in his discussion of the counsel of chastity in 1 Corinthians 7:32-34: "The unmarried man is anxious about the affairs of the Lord, how to please the Lord; but the married man is anxious about worldly affairs, how to please his wife, and his interests are divided. And the unmarried woman or girl is anxious about the affairs of the Lord, how to be holy in body and spirit; but the married woman is anxious about worldly affairs, how to please her husband." The life pointed to by the counsels can also be called better in that it has the potential to free us more from worldly cares and distractions. However, it is important to note that the counsels are not mandatory upon all, and it is not a sin to live other forms of life. In fact, God has not called everyone to the full embracing of all of these counsels. As St. Paul puts it (1 Corinthians 7:7), "each has his own special gift from God, one of one kind and one of another." God has given us all different gifts and callings, and the Church needs all of them. An obvious example is marriage. If everyone embraced celibacy, there would soon be no more Church on the earth at all! And there are many works and activities that God calls men to that could not be fulfilled if everyone embraced the fullness of all the counsels. The examples provided by those living other forms of life are important to the Church (marriage, for example, is a model of the relationship between Christ and the Church.) Therefore, while in a general sense, all other things being equal, we can say that the life called for by the full profession of the counsels is in some ways better, this life is not necessarily better for every individual person, nor would it be better for the Church or for the world if everyone tried to live the fullness of all the counsels. For some people, given their gifts, callings, talents, desires, personality, etc., it would not be best to choose to embrace all the counsels fully. It could even be sinful, if it would involve abandoning the callings and gifts God has given for those he has not. As the Catechism puts it (#1974), quoting St. Francis de Sales, "[God] does not want each person to keep all the counsels, but only those appropriate to the diversity of persons, times, opportunities, and strengths, as charity requires." Other forms of life not involving a full living of all the counsels are also good and pleasing to God, and necessary to humanity and to the Church, and they should not be considered inferior as if they were something to be shunned or avoided. Marriage, far from being denigrated, is even one of the seven sacraments! While a life devoted fully to all of the evangelical counsels can be in a special way freed from worldly cares and distractions, yet it has its own cares and distractions, and other forms of life have their own special blessings and means of sanctification.
Nevertheless, even those who are not called to the full embracing of all the counsels might be called to some of them, or to some of them to some degree. All of us are called to live out the spirit of them, as we live lives of full charity and devotion to God and his service in whatever way that makes sense to us in the peculiarities of God's individual call to each of us. Maintaining closeness to God and devoting ourselves to his service is something all of us should strive towards more and more in the context of our individual vocations.
This is another helpful article on the counsels, from The British Province of Carmelite Friars.
Published, appropriately, on the feast of St. Agnes
ADDENDUM 6/17/16: Pope Francis recently released an Apostolic Exhortation on marriage and family which devotes a short section to making the point that married life is not inferior to a life of celibacy. Here is a brief selection from Amoris Laetitia (Chapter 4, pp. 117-119--I've moved footnotes to within the text itself in brackets):
159. Virginity is a form of love. As a sign, it speaks to us of the coming of the Kingdom and the need for complete devotion to the cause of the Gospel (cf. 1 Cor 7:32). It is also a reflection of the fullness of heaven, where “they neither marry not are given in marriage” (Mt 22:30). Saint Paul recommended virginity because he expected Jesus’ imminent return and he wanted everyone to concentrate only on spreading the Gospel: “the appointed time has grown very short” (1 Cor 7:29). Nonetheless, he made it clear that this was his personal opinion and preference (cf. 1 Cor 7:6-9), not something demanded by Christ: “I have no command in the Lord” (1 Cor 7:25). All the same, he recognized the value of the different callings: “Each has his or her own special gift from God, one of one kind and one of another” (1 Cor 7:7). Reflecting on this, Saint John Paul II noted that the biblical texts “give no reason to assert the ‘inferiority’ of marriage, nor the ‘superiority’ of virginity or celibacy” [Catechesis (14 April 1982), 1: Insegnamenti V/1 (1982), 1176.] based on sexual abstinence. Rather than speak absolutely of the superiority of virginity, it should be enough to point out that the different states of life complement one another, and consequently that some can be more perfect in one way and others in another. Alexander of Hales, for example, stated that in one sense marriage may be considered superior to the other sacraments, inasmuch as it symbolizes the great reality of “Christ’s union with the Church, or the union of his divine and human natures”. [Glossa in quatuor libros sententiarum Petri Lombardi, IV, XXVI, 2 (Quaracchi, 1957, 446).]
160. Consequently, “it is not a matter of diminishing the value of matrimony in favour of continence”. [John Paul II, Catechesis (7 April 1982), 2: Insegnamenti V/1 (1982), 1127.] “There is no basis for playing one off against the other… If, following a certain theological tradition, one speaks of a ‘state of perfection’ (status perfectionis), this has to do not with continence in itself, but with the entirety of a life based on the evangelical counsels”. [Id., Catechesis (14 April 1982), 3: Insegnamenti V/1 (1982), 1177.] A married person can experience the highest degree of charity and thus “reach the perfection which flows from charity, through fidelity to the spirit of those counsels. Such perfection is possible and accessible to every man and woman”. [Ibid.]
Also, the Franciscan Media Saint of the Day blurb on St. Francis de Sales has a nice quotation from him making a similar point:
It is an error, or rather a heresy, to say devotion is incompatible with the life of a soldier, a tradesman, a prince, or a married woman.... It has happened that many have lost perfection in the desert who had preserved it in the world.