A UTXO, or Unspent Transaction Output, defines a spendable unit of ABTC. Every UTXO, when spent, is effectively destroyed and replaced with multiple other UTXOs of different values (see simplified example below), a process analogous to smelting and re-forging physical coins each time they are spent (impractical in the physical world, but easy when working with bits of data).
UTXO #1 (1 ABTC)
UTXO #2 (0.25 ABTC) UTXO #3 (0.75 ABTC)
With this in mind, the UTXO Set is the set of all UTXOs and defines all spendable ABTC units. Every ABTC node is capable of independently and trustlessly verifying the entire UTXO Set.