Homology is still a relatively
fuzzy concept in
biology. Generally, biologists consider homology to be the similarity of two things (behaviors, structures, genes) due to
common descent. In other words, the
common ancestor of these two species should have had this thing, which was passed down to those two (
modern day) species. Homology in this sense in contrasted with multiple independent origins. For example, the wings of insects and the wings of birds are typically taken to be
not homologous, because the
common ancestor of insects and birds did not have wings. This was all fine and well until developmental genetics came along...
Developmental genetics has shown us that while wings in these two groups were derived independently, many of the same genes are used to build these two structures. With this new understanding, we are left in a quandary over whether the wings in these species are really derived independently or not- it seems that they are partially homologous (ie partially similar due to common descent).
The reverse case is also a problem: how similar must two things be to be homologous? For example, genes can take on new functions in new species. This gene might be doing different things in two species, but it is present in both of them due to common descent. How different can the two genes be and still be homologous? These are open questions in biology, and are sure to be active areas of research and debate in the near future. Let us know if you have any thoughts...
Finally, this term is often used by molecular biologists when comparing how similar to DNA sequences are. For example, they might say that two genes are "40% homologous", meaning that they have identical bases at 40% of their sites. While it is possible for two genes to be only partially identical by descent (say due to horizontal gene transfer), this is usually not what has occurred in the typical molecular biology use.