See a list of users with rollback rights here.
Anyone can revert vandalism and bad-faith edits, but it takes a couple of clicks in the page history to get it done. Users with the "rollback" permission are able to undo bad edits with one click, by using the rollback link on diff pages and user contributions list. They are just like regular users with one extra button.
On Avatar Wiki, experienced users with a strong history of contributions and a history of anti-vandalism work may be granted rollback rights by requesting it at Requests for Rollback.
Rollback rights are a prerequisite for nomination on Requests for Adminship.