Moral Hazard, in Layman's Terms

I sent along to my grandparents the interesting discussion on Marginal Revolution about kidnapping insurance. My grandpa replied:

Greg, don't get your grandma started on how auto insurance has escalated the price of repairing, say, a fender. Auto body work used to be fairly inexpensive because a good many people paid for it out of their own pocket. They cared. Does anyone care how much the insurance company has to pay to fix my fender? I guess kidnap insurance works the same way.

Papa

Economists call this phenomenon "moral hazard." A line from the Wikipedia entry describes it this way: "In insurance markets, moral hazard occurs when the behavior of the insured party changes in a way that raises costs for the insurer, since the insured party no longer bears the full costs of that behavior."