Homology refers to common ancestry of two or more genes or gene products that have evolved from the same feature in the last common ancestor of the species. When applied to nucleotide or protein sequences, homology refers specifically to this relationship due to descent from a common ancestral sequence.
Homologous features are derived through the same evolutionary or phylogenetic origin, yet do not necessarily share the same function or structure. Homologous genes share an arbitrary threshold level of similarity determined by alignment of matching bases. Such homology is an important organizing principle for genomic studies because structural and functional similarities tend to change together along the structure of homology relationships. It may be difficult to determine that genes share a common ancestor when their structure has been modified through descent. Functional genes often display homology across species because evolutionary tinkering that destroys essential functions could be detrimental to the survival of the organism, and hence to transmission of the altered gene.
Homology is a qualitative term (+/-), while similarity is the corresponding quantitative term in that we refer to degrees of similarity. Homology is distinguished from homoplasy, which refers to the similarity between structures that is due to common ancestry. In cladistics, both homology and homoplasy are determined a posteriori with reference to a particular phylogeny that maximizes homology and minimizes homoplasy. The amount of homology between species may be used to determine evolutionary relationships and degrees of divergence.
Homeobox genes provide an example of functional conservation that is misapplied by creationists to refute biological evolution. Hox genes control early development and necessarily show high degrees of homology across species.