In airline parlance, to bump is to deny a passenger boarding with a valid ticket, often due to an oversold flight.
Many times, an airline will sell more than 100% of available seating, with the assumption that a small percentage may not show up (due to tardiness, cancellation, etc.). Bumping may be voluntary or involuntary.
Usually, when an airline acknowledges that a flight is overbooked, it first asks if any passengers will volunteer be bumped to a later flight. Passengers who get bumped can negotiate compensation, such as a voucher towards another flight, lodging and accommodations, and meals during the bumped period, especially if overnight.
If an airline cannot get enough passengers to volunteer, a passenger may be bumped involuntarily, though these passengers would be allowed to get the federal minimum compensation for it. Some frequent fliers craftily get bumped on purpose, constantly looking to be bumped in order to receive compensation.