Culpability is a state of guilt or responsibility. A lot of lawsuits are about who has culpability for something that went wrong.
Culpability is a fancy-sounding word, but it's a simple concept: guilt. You have culpability if you're responsible for something, usually something bad. If you left the door open and your house was robbed, you have some culpability (not as much as the robber, though). If a store owner doesn't salt the ice on the sidewalk and you slip, he has some culpability if you get injured. Figuring out culpability is about figuring out who's to blame.