This sermon, and others like it, was designed to be a wake up call intended to make people take religion more seriously. Full membership in the puritan church required a conversion experience. However, over subsequent generations, descendants did not have the same conversion experiences and were seemed (to the church authorities) to be living less spiritual lives. So, the church started the "Half-Way Covenant" where children of those who had conversion experiences could be partial members of the church. The hope was that partial members would eventually be persuaded to become full members via having a true religious conversion experiences. In a sense, this meant something similar to being "born again," a term that we use today.
However, preachers like Edwards thought this was too lenient and accommodating. Therefore, he tried to scare people into having a genuine conversion experience as soon as possible. For Edwards, this is the only way for a person to be saved.
He claims that men/women will slip and God will not save them. In other words, he is saying that they will slip unless they convert. "Their foot shall slide in due time." Without a conversion, the person will fall:
Unconverted men walk over the pit of hell on a rotten covering, and there are innumerable places in this covering so weak that they will not bear their weight, and these places are not seen.
Edwards repeats the danger of being unconverted. "The use of this awful subject may be for awakening unconverted persons in this congregation." Again, the sermon is meant to be a wake up call. This is why it is so laden with fear tactics and threatening language.