Basically, there are no extra features in the app, since its main goal is to provide the core features of Stack Exchange sites, only via an app which makes it more mobile friendly.
However, being an app gives it a benefit that might be considered a feature: push notifications. This means instant push notification for every inbox item you receive in Stack Exchange. In the ordinary site, you can set unread items to be emailed after several hours, but other than that, no instant notification if you're not viewing SE site at the moment.
Other than the push notifications, I can think of couple of other things that exist in the app but not in the site itself:
- Reply to comments: you can tap a comment, and a "Reply" icon appears that when tapped cause the comment author name to be automatically added with
@ in front of it. Site offers the autocomplete feature, but it's not really the same.
- Feed: not sure how exactly it works, but the Feed we have in the app does not exist in the site. It's a mix of hot network questions, with questions that might be of interest to you.
The above are not really "features", in my opinion, more like "nice to have" things.