When you get in-game achievements, you can earn experience points (XP) and levels on your Play Games profile.
When you're playing a game, you'll see a notification when you've earned XP or enough points to level up your Play Games profile. When you level up, you'll also see a notification in your mobile device's notification shade near the top of your screen and your Play Games Inbox menu.
You can view your XP and individual achievements on games you use with Play Games on your Play Games profile page.
For more information on how to make your Game Profile public or private, go to Play games on your device.