Think of each UTXO as a coin. They can come in any denomination. Whenever you make a transaction, all the coins you're spending are melted down and you create (usually) two new coins of the appropriate denominations to pay the recipient and return the remainder to yourself.

For example if you have two coins of two and three bitcoins and want to pay Alice four, you melt your two coins and create a new coin to pay her and a second coin of one bitcoin value to keep.