An idea that a party that is protected in some way from risk will act differently than if they didn't have that protection. We encounter moral hazard every day - tenured professors becoming indifferent lecturers, people with theft insurance being less vigilant about where they park, salaried salespeople taking long breaks, and so on.
Moral hazard is usually applied to the insurance industry. Insurance companies worry that by offering payouts to protect against losses from accidents, they may actually encourage risk-taking, which results in them paying more in claims. Insurers fear that a "don't worry, it's insured" attitude leads to policyholders with collision insurance driving recklessly or fire insured homeowners smoking in bed.