On Wikidata, rollbackers are users who have the technical ability to undo edits with a single click. (The "undo" feature, which all non-blocked users have access to, requires confirming the edit.) With one click, they can undo all the edits made by the most recent editor of any item or page. Rollbackers cannot only undo part of a series of edits – to do that, they must use the "restore" button. (Or, outside of the mainspace and property namespace, one should click "edit" on the old revision of the page, and press "save".)
Rollback should only be used to revert vandalism and test edits. If the edit was a test, ideally you should leave a friendly note on the user's talk page, directing them to the Wikidata Sandbox. (In some cases, it might still be preferable to use "undo" and a custom summary when reverting test edits.) Rollback cannot be used with a custom summary unless you have a script in your common.js that allows this, so unless you have such a script, it should not be used to undo good-faith contributions that were not test edits. Remember that rollback marks your reverts as "minor".
Requesting rollback 
Rollback rights may be requested at Wikidata:Requests for permissions: Requests for rollbacker flag. Users may self-nominate, or nominate one another; however, users should not be given rollback if they do not want it, and non-self-nomination requests should be put on hold until the nominee comments accepting the nomination.
Administrators may add the rollbacker flag to the accounts of users who:
- are generally trusted members of the community, preferably with at least some history in working against vandalism, or
- have a strong history of combating vandalism on other projects, and have shown a satisfactory understanding of how Wikidata works.
In general, rollbackers should also be autopatrollers and autoconfirmed users. When adding rollback to the accounts of users who do not have one or both of these rights, administrators should adjust their flags accordingly (in the latter case, by adding the confirmed right).
A list of users with the rollbacker flag can be found at Special:ListUsers/rollbacker.