A simplicial complex is a Space with a Triangulation. Objects in the space made up of only the simplices in the triangulation of the space are called simplicial subcomplexes. When only simplicial complexes and subcomplexes are considered, defining Homology is particularly easy (and, in fact, combinatorial because of its finite/counting nature). This kind of homology is called Simplicial Homology.
See also Homology (Topology), Nerve, Simplicial Homology, Space, Triangulation