They have all the user rights as Content Moderators and Chat Moderators.
Locking (protecting) a page so it cannot be edited or renamed by users without admin rights or autoconfirmed status.
They can ban/block users who are vandalizing the wiki from editing.
A bureaucrat can make other users into bureaucrats or administrators on their own wiki.
Bureaucrats can also give users the ability to "rollback" edits not made in good faith.
The "founder" of a wiki, the person who first requested it, is given administrator access automatically. Founders are also given bureaucrat access so they can make any other user on their wiki an administrator or bureaucrat. For a complete list of users with administrator access, see Special:Listusers/sysop.
If the wiki is in need of new admins, there will be applications announced. Active editors will be the prime candidates.
What can administrators not do?
Administrators should not use their administrator powers to settle editing disputes; for example, to lock a page on a version he or she prefers in an editing dispute that isn't vandalism. Administrator powers should be used to help keep the wiki clear of vandalism, spam, and users who make malicious edits, but not for simple disagreements between users acting in good faith. Ideally, an admin shouldn't be considered "in charge". The ideal admin is just someone who is trusted to have a few extra buttons and to use them for the benefit of the Wikia community.