The short answer to this is economics: airlines want to make sure that every flight is as full as possible to maximize their profits. The reported reason why airlines routinely oversell their seats is to recover costs the airline incurs for seat cancellations and for travelers who do not show up to take the flight. (On any given flight, some number of previously allocated seats go empty just before departure.) Empty seats are not profitable, so overbooking allows the airline to ensure that every seat on the airplane is making money for them. The “no-show rate,” which helps airlines determine how many extra tickets to sell, is determined by data from past flights connecting the same points. For example, if the data from most of an airline’s flights from Phoenix to Houston indicate that five passengers typically do not show up for the flight, the airline will sell five additional tickets. Such calculations are not perfect, and sometimes more people show up for the flight than there are seats on the aircraft, which forces the bumped passengers and the airline to work out an arrangement (such as rebooking on a later flight or remunerating with air-travel vouchers or cash) before the flight can depart.
The overbooking process is also said to benefit people who purchase last-minute tickets. If a flight has extra seats available before the flight leaves the gate, these can be sold at discounted rates, which allows the airline to garner some of the revenue that they would otherwise have lost. However, all seats are not equal. Passengers in the coach and business classes of a flight are the ones that are bumped most often. Airlines rarely choose to risk the ire of those traveling first-class, because first-class seats produce the most revenue per flight. In addition, frequent fliers, passengers who check in to the flight early, and those whose air-travel itinerary would be most disrupted by being bumped have greater clout in these situations than the occasional traveler or the traveler who checks in just before departure time.