A UTXO, or Unspent Transaction Output, defines a spendable unit of Alpha. 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 ALPHA)
↓
spend (destroy)
↓
UTXO #2 (0.25 ALPHA)
UTXO #3 (0.75 ALPHA)
UTXO #1 (1 ALPHA)
→
spend (destroy)
→
UTXO #2 (0.25 ALPHA) UTXO #3 (0.75 ALPHA)
With this in mind, the UTXO Set is the set of all UTXOs and defines all spendable ALPHA units.
Note ALPHA is not designed for transactions. The number of UTXOs should closely approximate the number of blocks
(Note that the verification process can be quite slow, depending on the node's hardware configuration and indexing options used.)