A lot of the functionality is very similar to what was in the PS app as well (not surprisingly.) There are second screen options to "enhance" the games you play or movies you watch, you can use the app to navigate the system, and control media. A nice addition is that you can use the app to surf the web on your TV, which is cool.
Of course, there are also things that you can do even when you aren't at home, including tracking achievements, messaging friends, watching game clips, and getting help in your games. One of the best features though is that you can browse content and pin it to your dashboard, so it will be waiting for you when you get back home.