When I am bored on the train, I open Quora's app on my iPhone to answer questions about branding. It is enjoyable and makes me feel like an "owner" of the brand. That is a personal example of how Quora's mobile app builds engagement with the brand for me - it turns me into one of the experts.
Similarly, I like the Drudge Report app because it lets me share news easily. The brand is about instant news updates, and by using the app I become a participant in generating that brand experience.
Twitter is probably the epitome of the mobile app building the brand as it offers real-time status updates created by you and those you follow.
Anytime you both use and create the brand using the mobile app, you are engaged in the brand experience.
(cross-posted from my answer at Quora)