It disappears... no, only joking.
![Tongue](https://bitcointalk.org/Smileys/default/tongue.gif)
Considering that all transaction confirmations and mining and the blockchain are not in any way dependent on YOUR computer... the transaction will complete successfully regardless of whether or not your computer is on, or your wallet is open and running.
How do you think paper wallets work? You can't exactly plug your piece of paper into the internet
![Roll Eyes](https://bitcointalk.org/Smileys/default/rolleyes.gif)
All the transactions are contained within the blockchain, which is nicely replicated across thousands and thousands and thousands of nodes around the world... they all contain the complete list of ALL bitcoin transactions that have ever happened. So, when you power your computer/phone/tablet back on... and reconnect it and sync up your wallet, any transactions received while offline will be found and added to your wallet.