In order to understand how Jonathan Edwards uses parallelism, one must first understand the context of the piece. First, this text is a sermon, an oral piece meant to be heard, not read. So speakers use particular techniques to aid their listeners in remembering the message being presented. Parallelism is one of those techniques (along with repetition and imagery).
Second, Edwards uses parallelism for different purposes for his message. For instance, Edwards proclaims to the church congregation: "The Wrath of God burns against [the unconverted], their Damnation don’t slumber, the Pit is prepared, the Fire is made ready, the Furnace is now hot, ready to receive them, the Flames do now rage and glow." Here, Edwards is describing, metaphorically, to his audience about the imminent danger that is God's wrath and the fires of Hell. By listing all the ways that the unconverted are nearing their doom, he is emphasizes the urgency for sinners to change their ways.
Another way that Edwards uses parallelism is through the logical appeal. Because Edwards wants to convince his audience to convert immediately to a more Christian life, he must not just scare them into converting but also convince them through rationalization: "The bigger Part of those that heretofore have lived under the same Means of Grace, and are now dead, are undoubtedly gone to Hell: and it was not because they were not as wise as those that are now alive: it was not because they did not lay out Matters as well for themselves to secure their own escape." In this example, Edwards gives evidence as to how those who appear on the outside to be good and holy are not necessarily saved from God's wrath. This evidence may not be proven factually, but because the congregation is comprised of believers who invited Edwards to preach to them, then he will convince them with this logic.