Badges

Getting a badge means you've completed a specific location on the main quest. To get the badge, you have to have completed the Battle Hall of that location. You can see what the highest level raid people have completed by looking at their profile! It's to the left of the avatar image.

Summery
To complete each of the main quest sites, you have to earn the "badge" of that site. This involves completing all the given quests as well as defeating the boss monsters in the location's hall with your troop or a group.