To grant a player OP type:

/op playername

Example: If the players name is bob you would type: /op bob while in game or in the console.

To DEOP a player type:

/deop playername

Example: If the players name is bob you would type: /deop bob while in game or in the console.


Notes From Minecraftwiki:

An Operator, also known as moderator, is a player designated to moderate a multiplayer server by the admins and the owner of the server. 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 operator by using the /op <playername> command, or by editing "ops.txt" text file in the server, then restarting the server. Operators 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.

Operators have access to all commands meaning they can stop the server, use the /give command, change gamemodes, 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 admins, the server owner, griefers and non-opped players.