As in some martial arts, belts mark the attainment of higher and higher levels within the gaming group.
They are assigned to users by the algorithm based on match results, group members' ree scores and the group's characteristics.
Once you earn a belt you'll never lose it, until you replace it with a higher-level one.
The belts are, in order:
Each belt is accompanied by a quotation from Yamamoto Tsunetomo's Hagakure.
More info about rankade badges here.