There are 3 kinds of Badges:
1. Apprentice Badges are worth 1 Star. These are the first badges you will earn when playing a level for the first time. After you have beaten all 5 levels of a location (like "Laguna Beach"), new levels will appear that are more challenging and will give you the opportunity to earn Expert Badges.
2. Expert Badges are worth 2 Stars. After you have beaten all 5 levels of a location earning Expert Badges, more levels and the most challenging levels will appear to earn Zen Master Badges.
3. Zen Master Badges are worth 3 Stars. These are the top badges!
Stars are needed for Star-Gates!