A server is a computer that hosts 8Realms and is maintained and operated by Jagex. There are currently five servers which can be played on:
Each of these servers contains various player-made empires which can be viewed with the World Map. The server's are most likely run independly from each other. The server you are playing on can be determined by viewing the World Map and looking in the south-east corner of the map, along with your settlement's coordinates. You can also change between servers by highlighting your empire's name located in the top-right corner and selecting any of the available servers from the list, as long as other servers are online and playable.
So far, 8Realms has experienced several server crashes, but this is to be expected as the game is still a Closed Beta. During the numerous crashes, players could not load the game, but could still access the forums.