What it checks
Every printed balance against the previous one, using the transaction between them. On a statement of 250 rows that is 249 separate arithmetic proofs.
What it catches
An amount that was edited, a row that was deleted, a row that was inserted. Each one breaks every total after it, so a single change shows up as a chain of failures.
What it cannot do
Prove a statement is genuine. Someone who recalculates every balance after editing produces a document that passes. This tells you what the arithmetic says, not who is honest.