In essence, the idea is this:
If a person does one act, and with that one act incurs two different kinds of penalties, we only apply the stricter one. So if a person (for example) borrows a cow and then slaughters it on Shabbos, he incurs two penalties: monetary restitution to the owner of the cow, and the death penalty for violating Shabbos. In this case, Beis Din only applies the stricter punishement, death, and the lesser one, the money, is waived.
Again, there are other details and complexities, but this is the general idea.
Can anybody give me a logical explanation for this concept? I don't think the transgressor could care less about the fine when he's dealing with the death penalty.