Historically, there has been a debate over how to translate this verse and render it from the Hebrew. The debate centers on whether God says "he" shall crush Satan's head or whether "she" shall crush Satan's head.
Now, it doesn't much matter since either reading is orthodox and true. Christ crushes the head of Satan absolutely, and Mary crushes the head of Satan by virtue of her role as the Mother of God and New Eve.
For Catholics, the "she" reading is the traditional reading of the Latin Vulgate and it is important because it highlights the importance of "the woman" (i.e. Mary) in human salvation. In other words, the "she shall crush" reading supports the Catholic argument that Mary's role as Mother of God makes her Mediatrix and her role as New Eve makes her Coredemptrix.
The obvious solution to this problem is simply to look at the original Hebrew. But that is where the problem begins. The medieval Hebrew Masoretic manuscripts read "he shall crush." (However, there are two Hebrew manuscripts that read "she shall crush.") However, there is good reason to doubt the majority Hebrew reading of "he shall crush."
Our three best Jewish witnesses to Gen 3:15 interpret the passage as "she shall crush." These are Philo Judaeus, Josephus the roman historian, and Moses Maimonides, the great medieval Jewish philosopher. Philo argues that the Hebrew parallel poetry of Gen 3:15 demands the reading of "she shall crush." Josephus, also writing in Greek, describes the passage for us as reading "she shall crush." Then last of all, Maimonides also states that Gen 3:15 teaches that the woman shall crush the head of the serpent.
So then, these three great Jewish scholars testify to the traditional Catholic reading of the Latin Vulgate. Why are the Hebrew manuscripts that we have today different from these ancient Jewish witnesses. The answer is that the Masoretic manuscript tradition has been corrupted - something claimed by the both the Eastern and Western Fathers throughout the centuries.
Even though I have previously used "he shall crush" in my first book and on this blog, I'm going to revert to the traditional reading of Gen 3:15 from herein out: "she shall crush your head."
"I will put enmities between thee and the woman, and thy seed and her seed: she shall crush thy head, and thou shalt lie in wait for her heel" (Gen 3:15).
O Mary conceived without sin, pray for us who have recourse to thee.