Imagine a spreadsheet with columns A for sender, B receiver, C amount, and D send_to_next. When Alice sends Bob bitcoin a new row is added with Alice in column A, Bob in column B, the amount in C and D is blank. In an existing row with Alice in column B, Bob is added to D. So if D is blank it is unspent. If you sum up all the amounts where Bob is in column B, and D is blank, you get Bob's bitcoin balance. These rows are the UTXOs.