What does the Catholic Church mean when it says In-vitro Fertilization separates the procreative act from procreation?

Humans are indisputably biological beings, and therefore (like so many biological beings) indisputably sexual beings. God, having created us as sexual beings, "saw that [everything] was very good" (cf. Genesis 1:31). The Church has always held the official belief (whatever individual bishops, priests, and theologians have said) that sex as an act is not sinful in itself, and that sex between spouses is in fact a good thing. Thomas Aquinas, in the Summa Theologica, discusses the question "Whether no venereal act can be without sin?" (i.e. "Is sex always sinful?") He concludes,

Just as the preservation of the bodily nature of one individual is a true good, so, too, is the preservation of the nature of the human species a very great good. And just as the use of food is directed to the preservation of life in the individual, so is the use of venereal acts directed to the preservation of the whole human race. Hence Augustine says (De Bono Conjug. xvi): "What food is to a man's well being, such is sexual intercourse to the welfare of the whole human race." Wherefore just as the use of food can be without sin, if it be taken in due manner and order, as required for the welfare of the body, so also the use of venereal acts can be without sin, provided they be performed in due manner and order, in keeping with the end of human procreation.

(Second Part of the Second Part, Question 153 Article 2)

The Catechism of the Catholic Church adds:

Sexuality is ordered to the conjugal love of man and woman. In marriage the physical intimacy of the spouses becomes a sign and pledge of spiritual communion.

(paragraph 2360)

And it continues:

Fecundity is a gift, an end of marriage, for conjugal love naturally tends to be fruitful. A child does not come from outside as something added on to the mutual love of the spouses, but springs from the very heart of that mutual giving, as its fruit and fulfillment. So the Church, which is "on the side of life," teaches that "it is necessary that each and every marriage act remain ordered per se to the procreation of human life." "This particular doctrine, expounded on numerous occasions by the Magisterium, is based on the inseparable connection, established by God, which man on his own initiative may not break, between the unitive significance and the procreative significance which are both inherent to the marriage act."

(paragraph 2366—the quotes are taken from the encyclical Humanae Vitae of Pope Paul VI)

The Church thus believes that it is wrong, because it is a rejection of the gift God has given us since the Creation, to do anything that is primarily intended to separate the sexual act itself from the concept of procreation. This includes both activities which are primarily intended to allow sexual activity without the possibility of procreation, and activities which are primarily intended to allow procreation without sexual activity. It is for this reason that the Church states:

Techniques that entail the dissociation of husband and wife, by the intrusion of a person other than the couple (donation of sperm or ovum, surrogate uterus), are gravely immoral. These techniques (heterologous artificial insemination and fertilization) infringe the child’s right to be born of a father and mother known to him and bound to each other by marriage. They betray the spouses’ "right to become a father and a mother only through each other."

(paragraph 2376—the quotation is from Donum Vitae, a letter of the Congregation for the Doctrine of the Faith)

This does, of course, bring up the question of why these techniques are wrong, but adoption (which could be considered a form of "surrogate uterus") is acceptable. Neither the Catechism nor the Summa directly address this question. However, the United States Conference of Catholic Bishops issued a "teaching statement" in November 2009 titled "Life-Giving Love in an Age of Technology". This document directly addresses the issue of surrogate parenting; it states that one of the moral problems with it is that

in an important sense, the spouses have decided not to be fully the mother and father of their child, because they have delegated part of their role to others.

In adoption, a specific delegation of that sort does not occur. The couple indeed becomes the parent of a child who (in the words of the document) "is not the fruit of the spouses’ commitment to procreate only with and through one another"; however, the conception of the child was not (as surrogate motherhood is) an evasion or deliberate delegation of the natural relationship between husband and wife, between parent and child.