In Edwards's "Application" section of the sermon, he gives the following image of the spider: 

if God should let you go, you would immediately sink and swiftly descend and plunge into the bottomless gulf, and your healthy constitution, and your own care and prudence, and best contrivance, and all your righteousness, would have no more influence to uphold you and keep you out of hell, than a spider's web would have to stop a falling rock.

Edwards uses this image of the spider's web, an object that even today's reader would understand in its simplicity, to reveal to his audience how insignificant their lives are. Just as we might wipe away a spider's web or swat at it in the woods, so, too, will God in His power be able to swipe all of humanity away in a single stroke. Humanity's "healthy constitution...prudence...best contrivance...righteousness" would act as the spider's web and be unable withstand a rock (humanity) from falling through.

Edwards again uses the image of the spider thus: "The God that holds you over the pit of hell, much as one holds a spider, or some loathsome insect, over the fire, abhors you." This image refers not the spider's web but to the spider itself, which many saw as a pest even in Edwards's time. So, too, does God view humanity; we are pests to be exterminated or even tortured in the fires of Hell.