Puritans believe in Calvinist predestination. In a nutshell, God has known you for eternity. God knows what's going to happen and what you're going to do. God decided whether you will be saved or not before you were born. Your salvation/damnation happens through God's grace, not through your good works.
This presents a dilemma: Why be a good, hard-working citizen if you can't affect the final outcome? The answer is they came up with is clever and I'm going to greatly oversimplify it.
Basically, the Puritans believed that there are clues as to whether you are going to be saved. If you look at a guy and he's a hardworking, serious fellow, he's probably going to be saved. If the guy is lazy and frivolous he's probably damned.
Thus your immortal soul depends on working as hard as possible even though it's God's grace that saves you and not your works.