There are several realms in MudGate, and Icemire is the backbone of the world and where the first of all existing realms, to which all most other realms leads to.
In general, the inner realms in MudGate are relatively safe to visit, while the outer realms are often uncharted and outlawed. They may result in the loss of equipment on death or player vs player combat.
A realm is a crafted area that can either be your private realm or an open realm where you can meet other players. Dungeons are procedurally generated areas associated with a realm that can usually only be entered by a few players per instance.