Administrators (also known as sysops, or just admins) are people who have the technical ability to delete pages, block disrupting users and protect pages against new edits, among other things. A full list of rights included in the administrators group can be found at Special:ListGroupRights.
Who are the administrators?
An automated list of current administrators can be found at Special:ListUsers/sysop on any wiki. The project page Project:Administrators might have more info about administrators, and policies regarding the admin tools.
Can I become an admin?
It depends entirely on your local community and the estabilished policies over there. Some wikis have very strict requirements for candidates, while you can be easily granted administrator rights on another wiki. Check your wiki's local Project:Administrators page to find out more.
What should an admin never do?
An admin should never block users without a good reason. The same goes for page deletions and page protections/unprotections. Administrators should always be able to give a reason for their actions, both in the summary of the action, and per request at a later time.
If an admin however blocks a user or deletes content pages without a valid reason, it is considered an abuse of admin tools. In this case, the user might have his or her adminship revoked.