As St. Augustine said, the grace of God is hidden in the Old Testament and revealed in the New Testament. We find one such example in Genesis 3. Adam and Eve have just eaten the forbidden fruit. God asks Adam why he has done this, and Adam, setting a poor precedent for many future men, blames his wife. (He blames God, too--"the woman whom you put here with me"--as in, "I wouldn't have done it if you hadn't brought her along!) God then turns to Eve, who blames the serpent for tricking her--the very first instance of the "devil made me do it" defense. God then turns to the serpent. Here's the interesting part, prophetic in a way you might not catch.
God curses the serpent to crawl on its belly and eat dirt. Then God says, "I will put enmity between you and the woman, between your offspring and hers." That's the NAB translation, the one we use at Mass. But the Hebrew and Greek words there which are translated "offspring" are better translated as "seed." The Greek word for seed is "spermatos," or σπέρματος, if we want to have fun with it. This is the word usually used for what a man provides in the process of procreation. It is the only place in Scripture which speaks of the seed/σπέρματος of a woman, so it's unlikely to be some special turn of phrase that has a non-procreational meaning. What does this term "the seed of a woman" refer to?
The key is in what this seed of the woman will do. "He will strike at [the serpent's] head, and [the serpent] will strike at his heel." The serpent is Satan, as the Church has traditionally interpreted this text. Who strikes at Satan's head? Who defeats Satan? The one who was born from a woman, without the cooperation of a man; the one who can be said to be the "seed of a woman." It is Christ. Christ is the offspring of Mary, who is the New Eve (as St. Irenaeus calls her). Here, moments after the Fall of humanity into sin, God announces His plan of salvation, and hints at how it will happen. In Christ's Incarnation, we see that plan begin to come to fruition. That's the best bit of foreshadowing I've ever read.