In The Rolling Girls universe, a Best is a prophet (an individual who is claimed to have been contacted by the supernatural or the divine, and to speak for them, serving as an intermediary with humanity, delivering this newfound knowledge from the supernatural entity to other people) who leads a nation. A Best holds a lot of influence over the people of the particular nation they happen to rule, as the Rest are obligated to follow the Best's orders.
Not all Best are the same nor have similiar goals. This is exemplified in the plot of The Rolling Girls where the main cast are ordered by their Best to travel around Japan riding their motor cycles to mediate multiple battles between nations and clans as they emerge, therefore their Mosa is all about saving the world and peace whereas other Mosa are about creating conflict, probably so that they can accumulate more wealth and status.
Mosa are also shown to have various abilities unique to that Best.