A change message is a small template attached to a field in pass.json, written as changeMessage in the file. When that field's value changes in a push update, Apple Wallet shows the message on the lock screen with the new value substituted in. A points field with the template "You now have %@ points" produces a lock screen line reading "You now have 1,250 points" the moment the balance updates.
The elegance is that the notification is a property of the pass, not a separate messaging system. There is no app requesting notification permission and no push campaign to build; keeping the pass truthful is what generates the message. That makes change messages the quietest kind of loyalty communication: they only ever say something that just became true for that member.
Each field carries its own template, so a program chooses which changes speak and which stay silent. A balance ticking up on every purchase might update silently, while a tier field announces "Welcome to Gold." Wallets ultimately decide how notifications are presented and coalesced, so treat the message as a courtesy line, not a guaranteed impression.
Google Wallet approaches the same need differently, with messages attached to pass objects rather than field-level templates. A wallet platform abstracts the two, and the broader craft, what to announce and how often, is covered under lock screen messages.