In the most common usage of the term, a server is a world to which the Graal Client can connect. The word is somewhat misleading, since many worlds can be hosted on the same physical server, but it is prevalent nonetheless. The difference between the terms 'server' and a 'playerworld' is that the latter can't be used to refer to GraalOnline-operated worlds such as Graal Kingdoms. A playerworld is a server but a server is not necessarily a playerworld.
The term is also used to refer to the GServer that runs a given world.