That's a good question and it is indeed not explained on the official website yet.
GrapheneOS Apps app is where users can download and update Google Services Framework, Google Play services, Google Play Store, and GmsCompat config. The Apps app seamlessly updates apps. A GrapheneOS user doesn't need to press any special buttons, doesn't need to manually check for updates, and doesn't need to resolve any dialogue pop-ups in order to stay up-to-date.
On stock Android, Play Store is responsible for updating most of these. Google uses staged rollouts which means that some user receive updates before others. On GrapheneOS Play Store is not allowed to update itself. The reason behind it is because we test Sandboxed Google Play (and potentially add more shims) before deploying it for newer versions of Google Play.
Hope this answers your questions