Edwards states that:
whatever some have imagined and pretended about promises made to natural men's earnest seeking and knocking, it is plain and manifest, that whatever pains a natural man takes in religion, whatever prayers he makes, till he believes in Christ, God is under no manner of obligation to keep him a moment from eternal destruction.
By natural man, Edwards means any person who has not become a Christian and been saved by making a confession of faith that Christ is his lord.
Edwards is stating that the purpose of his sermon is to illustrate that an unsaved individual can at any moment be plunged into the fires of hell. Edwards goes to great pains to describe how the unsaved live: they are like people trying to cross over a great fire on a very rickety bridge that is missing planks: they could at any step fall through the rotting planks to perish horribly. Or they are like a spider dangled over a fire, or like people walking on an unstable shore, liable at any time to slip into the pit of a raging inferno.
Edwards is graphic in illustrating the plight of the unsaved. He does this to try to bring people to Christ. To him, there is no middle ground between eternal damnation and salvation.