How would you define canceled check.?

A canceled check is a check that has cleared your account and has been marked "canceled" by the bank. Such a check has been paid by the drawee bank (your bank) and endorsed by the payee (the person or company who issued the check to you), the payee's bank, and the Federal Reserve Bank. Canceled checks can be used as proof of payment. They are also usually requested by a new employer for proof of your direct-deposit routing information.

In the not-so-distant past, canceled checks were actually mailed back to bank account holders along with their monthly statements. These days, this is rare. It is much more common to see scanned miniature versions of the checks on bank statements, if anything.