Game server, that is also often referred to as host or shard, is a server that is used as a source of events in multiplayer video-games. It transmits all necessary data and allows clients (players) to connect to it and therefore to each other. Server allows to bring the same instance of the gaming world to all users and to update this world as a result of different user interactions with it.
For this purpose the dedicated server may be used. It simulates game worlds without support of direct input or output, if it is not required by some administrative tasks. All the players use client programs to connect to such server and get data.
The advantage of using the dedicated server for such purpose is that such servers are located in professional data-centers and therefore get much higher level of reliability and performance. Of course, dedicated server costs money. Sometimes these expenses lie on the shoulders of game developers (mainly console games), and sometimes even in guilds or clans in game. But in the end the dedicated server remains one of the most popular ways to play multiplayer video games.