As Investopedia explains, a "bounced check" is a slang term referring to a check that cannot be paid by the bank because the account on which the check was drawn has insufficient funds. Banks typically charge penalties to account holders who write checks that bounce.
According to Wikipedia, banks sometimes pay checks when the accounts on which they are written have insufficient funds to cover the payment, especially if the overdraft is small. Banks more often choose to dishonor checks, thereby refusing to pay them or "bouncing" them. When this occurs, the physical check is typically returned to the account holder, who then must make other payment arrangements with the person to whom he wrote the check originally.