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Once a cheque is approved and all appropriate accounts involved have been credited, the cheque is stamped with some kind of cancellation mark, such as a "paid" stamp. The cheque is now a cancelled cheque. Cancelled cheques are placed in the account holder's file. The account holder can request a copy of a cancelled cheque as proof of a payment. This is known as the cheque clearing cycle.

A cancelled check is one that has been approved, cleared for payment, and processed. It is proof that there was a transfer of funds, although a check in and of itself won't help prove what the funds were for.

I don't think they mean canceled, as in "not cashed or usable". They mean canceled as in "transaction complete, this instrument is no longer valid for further transactions". When you write a check and someone uses it, it gets sent to your bank to be canceled and stored/destroyed.