A server is any computer that is connected to a network that has files or resources (printers or applications) that can be accessed by other computers over that network.  That said there are many types of servers each with there own feature set.

File-Servers

File-server also known as a NAS (network attached storage) is any computer that stores files that can be accessed by other computers on the network.

Web-Server 

A web-server is just a server that can can be accessed from anywhere via the “Word Wide Web”.

Printer Server

A print-server is a computer that is connected to a printer. That computer manages print jobs for other computers on the network.

Media-Server

A media server is a computer that contains movies, music and photos that can by accessed by computers and media playing devices of all types. (TVs, game systems, stand alone players) A media server is also just a file-server.

Game-Server

A game-server is a computer that is host for the game at a LAN party.