Unspent Transaction Outputs (UTXOs) directly represent how much of a particular address' balance remains 'unspent' and the chain of ownership going back to the cryptoasset's origin. In Bitcoin and like systems, transactions happen by sending an entire 'bucket' (e.g., 1 BTC) to a receiver and receiving the change owed (as a UTXO). By extension, UTXOs is the way one can calculate and represent a certain user's BTC balance on the Bitcoin blockchain.
Since this model doesn't operate on an account balance (debit + credit) system like that of Ethereum, it is up to wallets to aggregate all of the addresses' unspent UTXOs for which a user has the keys and to figure out their total sum holdings. This makes the individual bitcoins much less fungible but makes it difficult to track the addresses holding those UTXOs.
The UTXO system is like a digital recreation of a cash economy. For example, Alice gives Bob 1 BTC, and the system now recognizes that there is 1 BTC signed to Bob that he hasn't yet given to anyone else. If Bob had already had 1 BTC, his blockchain balance would be 1 BTC + 1 BTC. Bob's Bitcoin balance is the sum of all bitcoin signed to him, similar to how all the fiat cash in Bob's leather wallet is the sum of all fiat cash given to him. If he wants to combine his two separate BTC, he must do so in another transaction, much like he needs to do if combining two $5 bills into a $10 bill.