Aspect of an organism's morphology that is equivalent in form to the morphology seen in ancestor species.
Homologous structures are aspects of an organism's morphology that are identical by descent, that is, which exists in that organism not because the species that organism is a part of "invented" that structure, but instead because that species retained this structure from its ancestors. Homologous structures, in other words, are morphological homologies.
Contrasting descent with modification, homologous structures are aspects of organisms that have descended with relatively little modification. Note that this is not to say that evolution does not impact homologous structures. Instead, the retention of homologous structures can be viewed, at least in part, as a consequence of stabilizing selection.
Note that vestigial structures are examples of homologous structures as too are similarities seen among embryos. In short, unless one has an ancestor species to compare to, such as may be found within the fossil record, then typically homologous structures are identified as morphologies that are shared among extant organisms.
Alternatively, contrast analogies, which are not homologous structures, that is, are not similar between two organisms because their common ancestor also shared that structure. Analogies instead represent similar solutions to similar ecological problems, but rather than solutions that are retained by stabilizing selection, they are solutions that are arrived at more or less independently as a consequence of convergent evolution.