When an iPhone adds a pass, it quietly calls the web service URL declared in the pass and registers itself: this device holds this pass, and here is a push token to notify when something changes. That record is a device registration, and it is the plumbing behind every live update a pass receives.
The flow afterwards is a cycle. The issuer changes something, a points balance, a tier, an offer, and sends a push notification for the pass. The wallet wakes up, asks the web service for the latest version of the pass, and swaps it in place. The member sees a current pass, and optionally a change message on the lock screen. Without a registration, a pass is frozen at the moment it was added.
Registrations are scoped to the pass type identifier, which gives them commercial weight: whoever operates the web service for that identifier holds the connection to every pass in every wallet. In a pass migration, exporting serial numbers, authentication tokens and device registrations, and repointing the web service, is what lets passes move to a new provider without members re-adding anything.
Registrations also end. When a member deletes a pass, the device unregisters, which is how issuers know a pass was removed. Google Wallet has no equivalent concept; its passes are objects updated server-side through the API.