One of the most interesting (on paper at least, I haven't tried it yet) features is the ability to watch replays from a variety of angles. Now when you and your buddies get into an argument over whether a receiver was in-bounds you won't have to rely on the referees, you can check out the play from different angles and decide for yourself.
There's also the "Next Gen Stats" feature. NFL players wear a Zebra tracking device in their shoulder pads, and receivers are placed around the stadium. This system can then track player movement and convert it into stats in real time. Coaches apparently already use this system, but now it'll be made available to those of us at home.
There's also Fantasy League support for NFL, Yahoo and CBS Fantasy Football Leagues.
What isn't in there, yet, is Game Pass support. I talked about the $100/year Game Pass service a few weeks ago. Game Pass is teased in the app but there's no way to sign into it; the Game Pass signup page still says its coming soon to Xbox so I assume this is just another feature that's not quite ready yet.
The What's New segment of the app urges you to plug an HDMI cable into your Xbox One (in other words, use the pass-through TV functionality) to get the most out of the app. I'm anxious to see how that works if I'm watching a game via cable; I assume I'll run the NFL app snapped while TV runs in the main window, and I guess that's where we'll see the enhanced stats and so forth. I'm looking forward to watching my first live game with all these features and learning more about how they'll work.
Unfortunately at this point Microsoft seems to be downplaying the new app. Rather than release solid information about it, they gave us a funny video that mentions the features without going into any kind of detail.