Confirmations represent the number of blocks in the blockchain that have been accepted by the network since the block that includes the transaction. In other words, it represents the difficulty of a double spend attack. With zero confirmations no proof of work has been done, so you can't tell if anyone considers the transaction valid. Even with a single transaction, it is possible for an attacker to pre-compute a single block.

It is generally accepted for most transactions that 6 confirmations represent enough security to assure the transition is valid.