The administrator, or admin of a server, is the person who takes responsibility of that server. It may be that the server is running from their machine, or that they simply have jurisdiction over a remote server, or in some cases part of one. To assign a player as admin, add the player name into the ops.txt file in the server directory, then restart the server.
The term "admin" is not interchangeable with "operator". An operator is a person designated by the original administrator or other operators, to patrol the server on their behalf.
Administrators have all of the commands available in Minecraft, and also the advantage of the tools available from the server software. Admins have control over the selection and implementation of the world, and can choose the settings for the room, such as the maximum number of players, players allowed from the same IP address, and the name and MOTD of the room. Admins can also enable ghosting; chatting via the console, without being logged into the server.
Admins can assign operators to help moderate the server. Operators have a wide access to server commands, including the ability to kick/ban admins, which could result to griefing. Admins must take this responsibility seriously and only grant trusted and well-known players as operators. Admins can also use a permissions plugin to limit specific operators on certain commands.
Despite all these privileges, admins can still have limitations enforced by the server owner. This can be achieved using a permissions plugin. If admins abuse their power, they may be removed by the owner or fellow admins. On certain servers, admins do not have access to the console itself.