If you also have an Xbox like I do then it's a great way to stay connected across devices.
Basically the Xbox app allows you to access Xbox Live and send messages, join party chats, make purchases, etc., while sitting on your PC.
It also allows cross-platform play on multi-platform games such as Killer Instinct. When you purchase certain games on the Xbox you get a copy for the PC on your account as well and vice-versa.
The final thing is for games not on the PC, the app allows you to stream them from a connected Xbox on your network.