Anyone can tick a box. Verification is what turns a checklist into proof that the game is on your shelf.
Most boxed games have a barcode on the back. Scan it in the app and it matches the game to your list.
Loose discs and cartridges often have no barcode. Newer consoles such as PS4 and Xbox One have a code printed on the disc label, and the app can check that instead.
As a last resort, a photo of the game can be checked by AI. It is only offered when the normal check cannot pass, and it rejects screens, printouts and cover-only pictures.
Only verified games count toward milestones, so a trophy means something when you share it.