A rollback is someone who has the ability to immediately undo edits, rename pages, and I believe they can close/delete messages and threads. It's basically an Admin with no deleting pages and blocking. Rollbacks don't have any rights on chat, however.
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, user contributions list, or the list of recent changes.
It is important to note that admins (including bureaucrats) already have rollback rights by default. The right can be optional for a user to have rollback and admin combined, but it will not add extra speed even with slower internet connections. Users with rollback rights are just users who are not necessarily an admin.
Rollbackers (users with Rollback rights) can be seen via Special:ListUsers, but they do not by default have any special title that appears on their user page.
I am posting this message on everyone's wall who participated in the "Rename the Wiki" discussions over the course of the past nine months. We are now down to the Final Round, which will end on April 5, 2014 at 2 a.m. eastern standard time. "Encyclopedia SpongeBobia" came out on top of all the suggestions to rename the wiki. We need to make an official decision on whether or not we change the name. You are invited to participate in the discussion and voice your opinion.