The biological term for a group of organisms that can interbreed is species. In the biological species concept, developed especially by Ernst Mayr, a species is a group whose members can potentially interbreed in nature and produce fertile offspring. Reproductive compatibility helps keep the group genetically connected while separating it from other groups.
The definition is clearest for sexually reproducing animals, but it has limits. Some closely related species can mate yet produce sterile hybrids, as horses and donkeys do when they produce mules. Other species reproduce asexually, so biologists may use genetic, evolutionary, ecological, or morphological species concepts instead.
Population is a common mix-up: it means members of the same species living in a particular area, not necessarily the entire species. A genus is a broader classification containing one or more related species, while an ecosystem includes organisms plus their physical environment. Species is the basic taxonomic rank immediately below genus.