How do confirmations work?
The first confirmation occurs when your transaction is processed into a block by a transaction processor (also known as a miner). Due to the peer-to-peer nature of the network, though, a second confirmation is required by a second transaction processor (which confirms the transactions for that block, and also confirms the previous block). Each subsequent confirmation builds on the previous ones and helps to secure the Bitcoin network as a whole.
This process helps prevent someone from copying a bitcoin and trying to spend the same bitcoin twice. After 6 confirmations, it will show as confirmed in your Bitcoin client; at this time the risk of double-spending has dropped to virtually zero.
Bitcoin will allow you to spend coins after just 2 confirmations, where the risk of double-spending is already very low, but you will have to pay a transaction fee to spend recently received coins. The longer you hold the coins, the less likely you are to need to pay a transaction fee to spend them. (You may also have to pay a transaction fee if you try to spend a large quantity of small coins, regardless of their age.)