It's when all the air goes out of the basketball. Just kidding...
When a mechanical switch is used as a data input, the contacts "bounce" upon contacting and un-contacting. This can cause havoc in digital systems. So either a network is used to insure only one of the bounces is sensed by the logic, or a software process is used to capture the correct logical level and ignore the bounces.
When a mechanical switch closes or opens, the contacts vibrate and open/close dozens of times in reality. Debounce means some way to electronically filter out the bounce to make a circuit function correctly.
More details to follow by other members, usually capacitor filters or software delays.
Tubeguy's link has an additional link to ONSemiconductor DATASHEET (MC14490) that describes debounce as: "the elimination of extraneous level changes that result when interfacing with mechanical contacts."
unfortunately, that is how they describe the chip's funnction - without ever saying the word, "debounce". I would never have thought of looking for a "bounce eliminator circuit". No wonder I have never heard of the chip nor seen it used in a circuit. Nobody knows it exists.