An associated app is the app a wallet pass declares as its own. Apple Wallet shows it on the back of the pass: a link to install the app if the member does not have it, or to open it if they do. pass.json declares it by App Store identifier, optionally with a launch URL so the app opens on the right screen. Google Wallet does the same through an app link on the pass object, rendered as a button on the pass.
It is optional, and that is the point. A pass does not need an app to be added, updated, presented or messaged; the wallet does all of that. The associated app exists for programs that also have an app and want the pass to route members into it, for example for booking, ordering or a fuller account view than the pass can show. For a program without an app, the slot stays empty and nothing is lost.
Where a program wants the pass to lead somewhere, there are lighter options than a full app. A deep link in a back field opens a web page or an app screen. Featured actions put those links on the pass face. An App Clip gives iPhone members an app-sized experience without an install. Each of those works with or without an associated app.
The practical question is which way the traffic should flow. Apps are good at pulling members into a wallet pass, since a pass added from inside an app is a pass a member chose. A pass is good at holding members without an app, since it stays in the wallet after the app is deleted. Programs that treat the pass as the primary surface, and the app as one destination it can point to, get both.