0/unconfirmed - the transaction has spread through the network to the destination. This happens almost instantly.
1/unconfirmed - a block passed while the transaction was unconfirmed. Reversing a transaction at this stage is extremely difficult. This takes 10 minutes.
X confirmations - a miner put the transaction into a signed block, and the transaction is official and irreversible. This takes 10 minutes to over an hour, although if a transaction fee is used the transaction will almost certainly be included in the first block.