Adam knew that he was different from the other animals and that he could not find his fulfillment in them. After God noted, "It is not good that the man should be alone," (Genesis 2:18), He "caused torpor to fall upon the man, who fell asleep; then he took one of his ribs and closed the flesh again in its place. With the rib that the Lord God had taken from the man he formed a woman" (Genesis 2:21-22). The Holy Father notes that Adam went to sleep dreaming of his future bride.
When he awoke, Adam exclaimed at the sight of Eve, "This time she is flesh from my flesh and bone from my bones" (Genesis 2:23). Adam sees in Eve a person to whom he can give a total gift of himself, and who in turn, can completely give of herself to him. Their bodies are literally created to go together.
Here is perhaps the most important part: "Man becomes an image of God not so much in the moment of solitude as in the moment of communion" (TOB, 163). What JPII is saying is that the marital love is an image of the Trinity. How so? Well, in the Trinity, we have God the Father and God the Son who love each other so totally, that their love results in a third Person -- the Holy Spirit. With a married couple, we have a husband and wife who love each other so completely that nine months later you may have to give that love a name. If they are open to life, their love may be manifested in the gift of a third person -- a baby.
In a Vatican II document, "Gaudium et Spes," the Church said that only by sincerely giving a gift of oneself can one discover himself. When man and woman were created, they realized that they were created as a gift from God in order to be a gift to another. Thousands of years later, and with the introduction of sin, we still are created as a gift from God in order to be a gift to others. We can give a sincere gift of self in many ways (volunteer work, helping around the house, praying for others) but the way which most closely images the Trinity (though it's still a long, long way form adequately expressing the life of God) is through married sex.