This represents the advancement of a specific unit group's level. Tap the Mastery button when conditions have been fulfilled to raise its level and claim level rewards. You can check which units Mastery effects are applied to by tapping on Unit List.
Raising the aggregate level of Mastery within a group will unlock Mastery effects, which grant bonuses to your units. Mastery effects can be stacked with other Mastery effects. You can view the active Mastery effects by tapping on Active Effects.