If you complete all maps from a zone with 3 stars on the 3 difficulty settings, you'll unlock a bonus map.
There are 729 stars throughout 9 zones.
Stars are used to research and improve Tower Talents (each Talent level costs 3 Stars along with Tears of Shiva) at the Engineering Quarter, from Kingdom Level 30 onwards. They also have an effect on Kingdom Leaderboard, and through this on Kingdom Tax.
Not to be confused with Honor Star.