The Live Calendar tile shows you an overview of the coming appointments from the account you are logged in with.
Fromt the live tile, you can see detailed appointment information when you click on a appointment. From the bottom you can open the Calendar.
To activate the app:
Change the tile format to 4 x 4 to get live version.
When changed back to 2 x 2 or 1 x 1 format it will show the regular icon.