A cryptocurrency transaction is considered confirmed when it is included in a block on the blockchain. Each new block after the first one is an additional confirmation for that transaction.
Since there is no central authority to facilitate transactions in cryptocurrencies, they are instead processed by the network at large, or, more specifically, by the miners, who compile new transactions into blocks, secure them via the proof-of-work algorithm and add them to the blockchain.
Before a transaction (TX) can be recorded on the blockchain, it needs to be signaled to the network. Transactions that have been requested by users but have not yet been picked up by any miner and put into a new block are considered unconfirmed and are collected in the mempool — the backlog of all currently unconfirmed TXs.
As soon as an unconfirmed transaction does make it into a newly mined block, it receives one confirmation, or, in other words, becomes confirmed. After that, every new block that gets added to the chain becomes an additional confirmation for said transaction. So, for example, if a TX was confirmed in block number 656307 and the current block height is 656312, it has six confirmations.
The number of confirmations is important for security reasons: if a hacker wants to attack the blockchain by feeding it false transaction data, they need to break the security of each individual block in strict order, starting from the latest one in the chain. The more blocks have been mined since a particular transaction took place, the harder it is for a hacker to break through all of them and reverse that transaction.
Because of this, most crypto businesses that process customer transactions, such as wallets and exchanges, require at least three confirmations (or more, depending on their policy) before accepting a TX as truly valid and irreversible.