Here's the Catholic explanation:
Marriage has a threefold good and set of ends - children, the indissoluble unity of the spouses, and the holiness of the Sacrament. The form of the sacrament is the mutual consent of the spouses, and the matter is their bodies, so the Sacrament of Matrimony (or Holy Crowning if you will) is only completed by their coming together in sexual intercourse, and every time the spouses have sexual intercourse with each other, provided that grevious sins that cry to heaven such as sodomy, fellatio, and contraception are avoided, they can grow in grace because of the Sacrament. Their action is Holy because it signifies the union of Christ and his bride the Church.
Marriage was instituted, as Genesis teaches us, for the propagation of the human race within a stable family environment, and the creation of that stable family environment by the pleasure and attraction of sex between the husband and wife. Christ has blessed and raised this union to the dignity of a sacrament, whereby Christians can grow in grace by its reception and exercise to better support their children and each other towards salvation. So the crowning good of Holy Matrimony is the Holiness of the Sacrament, but its first end is children.
So Holy Matrimony, and sexual intercourse in Marriage, have three purposes.
The frustration of the natural first end of sex within Marriage, the conception of children, makes the entire Marriage into a lie. "When this is taken away, husbands are shameful lovers, wives are harlots, bridal chambers are brothels, fathers-in-law are pimps." (St. Augustine, Against Faustus 15:7, AD 400). (Note well that he says "taken away", not "absent" - the sin is in the human will, not defects in the human body such as sterility, or temporary inability because of pregnancy or the natural cycle of the woman.)
Because Matrimony signifies the union of Christ and His Church, contraception is the equivalent of Christ (the husband) or His Church (the wife) preventing His Church from gaining new offspring (pregnancy) through conversion (conception). As abominable and unimaginable as this blasphemy is, so is artificial contraception.
Sex and sexual desire was ordained BY GOD, and as long as it is within the Sacrament of Marriage, blessed by God...
But it must be exercised to the due ends and with due means. Simply because one is married does not make lawful that which is inherently unlawful, such as the abominable peversion of sodomy. Lust is a vice, not a virtue, even within Marriage. It is laudable to want sexual union with ones wife as an exercise of the holy union between husband and wife or for children, and the pleasure attached to it is a blessing from God when enjoyed in these bounds. It is a fault to wish it for sensual pleasure alone though, because that is no different than fornication, and this is intrinsically what artificial contraception does, because it frsutrates one of the ends which must always be present (as regards sex during pregnancy, the openness to children during sex has already occurred to cause the pregnancy, therefore it suffices that the spouses come together to signify their union; the openness to children is implicit in the physical circumstances of the woman).
I believe it says in the Scripture, "The marriage Bed is undefiled"
"Marriage is to be held in honor among all, and the marriage bed is to be undefiled; for fornicators and adulterers God will judge." (Hebrews 13.4). It is not saying "do whatever you will", but rather, "keep your marriage bed pure". You cannot keep it pure by using contraceptives, or by other common perversions like rectal intercourse, coitus interruptus (withdrawal), consummated fellatio, and mutual consummated masturbation. Simply put, husband and wife are free within marriage to caress and kiss each other as they will, but if they continue to the point where they wish to or will have an orgasm, the husband MUST climax inside the woman's vagina without artificial barriers or drugs in the way to prevent conception. Otherwise, they have sinned.