"Superspace" is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom.
See also supermanifold (although the definition of a superspace as a supermanifold here does not agree with the definition used in that article).
Rm|n is the Z2-graded vector space with Rm as the even subspace and Rn as the odd subspace. The same definition applies to Cm|n.
The word "superspace" was first used by John Wheeler in an unrelated sense to describe the configuration space of general relativity; for example, this usage may be seen in his 1973 textbook Gravitation.