What is the Profile screen?
This is where you can see stats of a player. You can view your own profile by tapping your name on the top bar of most menus, and you can view other player's profiles by tapping the box to the right of their name and selecting "View Profile".
On the left, you will see a title which indicates the player's VIP status, and the player's name just below. The bottom left value indicates the player's level.
To the right, you will see their progress on Guns Owned, Upgrades, and Bosses Killed. The percentage at the top shows the overall completion of the previous three stats. Lastly in the bottom-right, you will see the latest Zone that they have reached in Campaign mode, and the last time they were online.