Operator

General
An Op, or operator, is a player designated to moderate a multiplayer server by the admin. This is done to help keep control of the server from unruly players and griefers, and even a reward to trusted players. People are made op by using the /op command. Ops have access to a variety of server commands which aid them in their policing duty. These are activated by typing them into the chat with appropriate arguments.

Ops also are granted the privilege of destroying and placing blocks. Although the admin can also decide to let all players destroy and place blocks.

Problems with untrustworthy Ops
Ops have access to all commands, meaning they can stop the server, control any plug-ins, such as spawning large amounts of mobs or removing entire chunks (when using server software that supports plug-ins) and kick/ban the admin, grief and kick/ban players.

This can be avoided in Modded servers with any permissions plug-in. This disallows some Ops the right to use certain commands.