Confirmation means a cryptocurrency transaction has been verified (via the mining process) and added to a block that contains many other transaction.
Confirmations are more blocks containing many more transactions that have been added to the blockchain. Confirmation time varies between cryptocurrencies.
Bitcoin has a confirmation time of about 10 minutes. This means that about every 10 minutes, your bitcoin transaction gets buried deeper within the blockchain, making it more difficult to alter.
Many exchanges will require multiple confirmations until the transaction is considered secure.