A bounce, quite simply, is a message that was sent but was not actually delivered.
Some common reasons for bounces are a destination email address that is no longer valid or a mail box which is full. Some other reasons for bounces are a failure of some sort with the receiving mail server or a mis-configured spam filter on the receiving end.
Think of a letter, perhaps with an incorrect address, dropped in the mailbox. The post office will attempt to deliver the letter, but perhaps the post office branch that is to handle the final delivery cannot complete the delivery. It will be returned to you as undeliverable - in other words, it bounced.
Do you remember the Elvis song Return to Sender? He described a bounce so much better than we ever could.