This diagram is the transaction as the database actually lives it: a sequence of in-memory changes that a file keeps honest. BEGIN only assigns an ID and a state. The real work happens in the buffer pool, where rows are modified in pages that may never reach disk during the transaction at all. What makes it a transaction is the write-ahead log. The database appends change records first, fsyncs them, and only then writes a commit record — the append-before-write ordering means the log is always ahead of the data pages. The fsync calls are the commit point; nothing counts as committed until the log says so durably.
The ordering matters because crash recovery reads the same log. Replay a committed transaction's records and the data pages are reconstructed; find a transaction with no commit record and everything it did is undone. ROLLBACK is the same machinery, run eagerly. Each stage in the diagram is a distinct mechanism — buffer pool, WAL append, fsync, commit record, visibility — and the boundaries between them are where durability is won or lost.