An incentive is something that motivates behavior. Typically, an incentive is something that encourages a certain behavior, whereas a disincentive is something that discourages a certain behavior.
Incentives are pivotal for the field of economics, because they drive economic decisions. Both positive and normative economic theories need to account for how humans respond to incentives, otherwise they will fail to accurately describe behavior.
A deterrent is a disincentive. One of the purposes of the justice system is to deter crimes.
Deterrents can be effective ways of shaping the behavior of societies. For example, suppose that every day, 1000 people commit action "X". If X is made a crime and punished accordingly, it will deter the behavior. A naive assumption is that the state will have to punish 1000 people a day. In fact, the state will need to punish significantly fewer, because many previous offenders will cease the activity in order to avoid the punishment.
A perverse incentive is an incentive that creates undesirable results.
For example, certain government and bureaucratic agencies have the perverse incentive to spend more than is necessary, because the budget allocated to them for the next year is based on how much they spend the previous year.
Another example is "welfare cliffs;" situations where increasing one's income will actually decrease their spending money when you take into account the affects of means-tested welfare programs.
A moral hazard is a problem derived from perverse or inappropriately set up incentives. For example, if an industry knows that it will be bailed out in the event that it fails, it will not take appropriate actions to avoid failure, because the potential for bailout lessens the forces disincentivizing failure.
Another appropriate precaution is that people will not take appropriate precaution because they know that their insurance covers damages.