A gaming server is a computer used to run a multiplayer game either over a local area network or via the internet. The speed is measured more often than not in ping rate (in milliseconds) and for a game to play at a reasonable rate you want to be at less than 400 although it is best to be significantly below this.
The server takes connections from other people with the game, provides a central point of connection and handles the flow of data between the players computers.