A person or organisation who has insurance cover may be be more prepared to take risks than someone who does not.
For example, someone whose car is insured against theft may be more careless about reducing the chances of theft than they would have been without such insurance.
This is partly why insurance companies require excesses (the amount of a claim paid by the person covered) on most claims, and reduce premiums quite sharply as excesses rise. It is also why insurers are very careful about the valuation of what they insure and why they are not legally required to pay more than the real value of what they cover, even if it has been insured for more.
Moral hazard can also occur outside insurance, although it is less of a concern. Banks and financial institutions often have implicit state guarantees (not formal or legally binding guarantees, but a general expectation that they are too big/important to fail). This creates an incentive for the management and shareholders to take bigger risks as they will benefit from gambles that work, but the state will pay for those that do not. This is similar to the agency conflict between shareholders and debt holders.