The file revision history is - to the best of my knowledge - an OS X API that applications have to use (opt in). I don't think it comes "for free" with an OS upgrade, unless you mean Time Machine.

Except that Microsoft Mac software neither follows OS X conventions (e.g. putting Office system files in the user's doc dir) nor implements many of the important features (e.g. leveraging the automatic file versioning introduced three years ago in OS X Lion).

The current version of Office Mac predates Lion, which is probably why it doesn't use Lion features.

How exactly can he check it? As a user of another OS, I'm asking to learn how this feature actually works.

It's easy. Right there in the File menu near the Save command is Revert To, which leads to a submenu with Previous Save and Browse All Versions... options. The latter uses the slick Time Machine UI (http://support.apple.com/kb/ht4753).

Except, per my other comment, Microsoft doesn't bother writing Mac software that works like Mac software. It's kind of like running Java desktop software (actually worse)... neither native feel nor integrated with the OS like other Mac apps.

As you say "Microsoft doesn't bother writing" and his girlfriend uses MS Word on OS X if I understood. Can she then use that feature to recover her work after she had done the "Save" from the MS Word or not?

No, she's probably not going to be able to recover her lost work. What OP and others are trying to point out is that OS X has support for saving revisions to documents if application developers (like Microsoft) would just take advantage of it.