A tier is a member's level in a program: the bronze, silver and gold of classic loyalty, or whatever names and thresholds a program chooses. Tiers turn accumulated behavior, usually a points balance or spend over a period, into a status the member holds, with better benefits attached the higher it goes.
On a wallet pass, tier is not a line in an account somewhere, it is on the pass itself: named in a field, often reflected in the pass design, and updated by push update the moment it changes. Reaching a new tier can announce itself on the lock screen, which is the difference between status a member has and status a member feels.
Tier also does work behind the scenes. As a segment rule, it targets campaigns: an offer for gold members only, a nudge for silver members close to the threshold. As an automation trigger, a tier change can fire a message by itself, congratulations and new benefits the moment the member crosses the line, with no one pressing send.
The design questions matter more than the mechanics. Tiers earn their keep when the next level is visible and reachable, and when the benefits differ enough to want; a program where most members sit in the bottom tier forever is a points program wearing a costume. The pass helps here too: showing progress toward the next tier makes the ladder part of every glance at the pass.