It is a representation of the number of blocks present in the blockchain which are now accepted by the by the network since the block that includes the transaction. There is not actual authority to determine whether the transactions is valid or invalid, so the recipient uses number of confirmations as a way of protecting against double-spend attacks.
The network always try to extent the blockchain, so that some chain may win. The deeper the transaction is in the chain, the higher the chance it will win because the network tries very hard not to duplicate efforts. It is mandatory for the attacker to match the power of entire bitcoin network to get along with the block generation, as the difficulty level keeps on increasing with the increase in the block else it will get difficult for the hacker to forge the transaction.
Technically, the more nodes to confirm the transaction, the safer you are from any hacker. So feel please when more than 2 miners verify your transaction. As the more verifications, the higher are the chances that transaction will remain in the public hash chain rather than a conflicting transaction if there was one.