Generally speaking, realms are areas of space that are similar to verses, although they are less well defined. They can be non-physical, more subjective, transcendental in some ways, just very disconnected with the typical physical reality, etc.
Their nature is usually intimately related to that of its inhabitants and their reality can be fully defined by either the will of a single ruler of the entire realm (as can be the case with the realm of some god like entity), or by all the combined minds of its inhabitants.
This is not for usages of the geometrical meaning of the word realm which just means a space with three dimensions. Those can be found on the 3-dimensional category.