Here is some information on confirmations: https://en.bitcoin.it/wiki/Confirmation

Above Wiki has some good information regarding Bitcoin in general, it is a good place to start to learn details about how Bitcoin works.

In essence the number of confirmations is equivalent to the number of blocks deep the transaction sits in. As miners solve new blocks, they are strengthening the confirmation of your previous transactions. The further 'down' your transaction sits in the chain the less likely it is someone can double spend those outputs.  Described In Section 11 - https://bitcoin.org/bitcoin.pdf