It stands for "Unspent Transaction Output" and essentially it's just a receipt to prove that you own what you say you do. And your wallet is really just a collection of those receipts.
Whenever you spend a portion of one receipt, you destroy the original and get a new receipt for the amount you didn't spend and the recipient gets their own receipt. Likewise, if you spend from multiple receipts, they're all destroyed and the same process occurs.
The proof of ownership comes from your private key. Only that key can create a signature that matches the one on your receipts.