What is a Bitcoin confirmation?
A payment has one confirmation once it's in a block, and one more for each block after. The more it has, the harder it is to reverse.
With no confirmations, a payment is still waiting and is not final; it may be replaced. Once it's in a block, a chain reorganisationChain reorganisation (reorg)A replacement of recent blocks when nodes switch to a valid chain with more accumulated work. Recent confirmations can change. can still remove it. Reversing it would mean out-mining the rest of the network, and that gets harder with every block added.
Each service chooses how many confirmations it requires before crediting a deposit, and may apply other checks. Follow the recipient's policy rather than assuming one number fits every payment.
References
- Bitcoin Developer Guide, “Block Chain”.