Yesterday's United Airlines controversy served as an uncomfortable reminder that airlines routinely overbook flights. Everyone has seen it happen, even if they haven't seen anything as disturbing as that video or haven't had the misfortune of buying a ticket four months in advance only to get rerouted through Antarctica en route to Seattle.
TED-Ed has a video that goes into exactly why airlines and other businesses overbook appointments and tickets. The starting point is simply that many people never show up. It's nearly a guarantee that someone won't show up for their hotel booking, dentist appointment, or flight back to the Midwest for an awkward Thanksgiving.
But for the business to maximize their profits, they can use complex calculations to maximize the amount they're able to make with the foreknowledge that some people will be no-shows.
However, the calculation gets complicated. In part, that's because the amount a business makes on a single ticket — $250 in the video's example — is far less than the penalty they pay for bumping someone from their flight. Bumping someone from their flight often involves a refund, food, rebooking, or a hotel room.