UTXO
An accounting design where a balance is the sum of unspent chunks of coin, each spent whole like a banknote.
In this model, used by Bitcoin, a transaction consumes one or more unspent outputs entirely and creates new ones, including a change output back to the sender. The protocol never stores a balance for an address; wallet software computes what it displays by adding up the outputs it can spend. The design allows outputs to be validated independently and in parallel, and it makes it easy to use a fresh address for every receipt, which helps privacy. It is harder to build long-lived shared programs on, which is one reason chains aimed at smart contracts adopted accounts instead; Cardano's extended UTXO model is an attempt to combine the two.
In practice
Spending part of a UTXO requires consuming it in full and creating a change output back to the sender, the way breaking a banknote returns change.
The common misunderstanding
A UTXO chain does not store balances at all; the balance shown in a wallet is a total the software calculates and the protocol never records.