In Genesis 4, we have the story of the first family: Adam and Eve, their sons Cain and Abel, and then, after Cain murders Abel and is driven away, the third son, Seth. In the early church, pastors and writers found allegorical connections in this story with (1) the fallen nature of humanity, (2) the relation of Christ to Adam, and (3) the dynamic interweaving of persons within the Trinity.
The first connection is the simplest to see, largely because it's right there in the open. The story of Cain and Abel follows directly after the story of the Fall and the expulsion from the Garden of Eden, so it makes sense that we would then get a story about the effects of the Fall. Taken as a historical account, the murder of Abel is clearly illustrative of that very point. But the early church fathers also liked to look for allegorical dimensions, and they found a possible one in this story. If Cain represents human nature's sin and Abel represents our original good destiny, then the story of Cain and Abel can be taken as an allegory of what happened to us, to our deepest inner nature, in the Fall: our choice to sin destroyed our original good destiny. It did not, however, destroy our whole selves completely; and thus the exile of Cain represents our new destiny, now tied to our sinfulness: as wanderers and strangers in a broken world, a world that we should have ruled in goodness and godliness as the king-priests of the Creator.
The second connection is perhaps a bit more of a stretch. It has to do with the loss of Abel (the original good son) and then the birth of Seth. Early church writers saw in this a faint foreshadowing of the role of Christ himself. Adam was created "very good," but then fell into sin, and Christ was sent as "the new Adam" (to borrow a point from Paul's thought in the New Testament). The birth of Seth after Abel's demise (which is described in Gen. 4:25 as a replacement of Abel) was taken as a prefiguration of the birth of Christ after Adam's sin. It was also sometimes connected to the resurrection of Christ, simply because this story--the first story in which a "son" of any kind appears--shows the loss of a son, immediately followed by gaining a son back again.
The third connection (also a bit of a stretch) focuses on the biblical language having to do with the creation of Adam, Eve, and Seth. After the story of Cain and Abel, with its allegory of human fallenness, we get the actual "first family," the one that will go on to represent the covenant-community of God: Adam, Eve, and Seth. (Interestingly, Seth got picked up by many extrabiblical accounts in the ancient world as a prominent character representing mystical knowledge of God.) We begin with Adam as the source of humanity, since he was created specially by God. Next came Eve, who was created from one of Adam's ribs. And then there was Seth, who in Gen. 5:3 is described as having been "begotten." The early church fathers noted that the unusual pattern of creation in this first family matched what Christian theology had come to understand about the interwoven relationships within the Trinitarian Godhead: God the Father was seen as the uncreated source (as Adam was the source of humanity); God the Son/Jesus was understood to be "eternally begotten of the Father" (just as Seth was begotten); and the Holy Spirit was said to "proceed" from the Father (just as Eve, in a sense, "proceeded" from Adam by means of his rib). It's an imperfect analogy, of course (as all analogies of the Trinity are), since the traditional descriptions of the Trinitarian relationships are not meant to imply that the Son and the Holy Spirit were brought into existence from nonexistence, whereas this is definitely what happens with Eve and Seth in the biblical account. But with that aside, it's an interesting parallel nonetheless. Again, this may simply be a case of the early church fathers just finding what they wanted to find, but if nothing else, it certainly represents an interesting exploration of the early Genesis accounts.