What happens when someone sends me Waves but my computer is powered off?

Waves are not actually “sent” to your Wallet, the coins are in the network marked as sended to you; the software only uses that term so that we can use the currency without having to learn new concepts. Your wallet is only needed when you wish to spend Waves that you’ve received.

If you are receiving coins when your wallet client program is not running, and you later launch the wallet client program and login, the coins will appear in your wallet.

So, you don’t need to stay logged in to receive Waves.