Homology mean any similarity between characters that is due to their shared ancestry. The term homologs looks simple theoretically but its important to get the various terms clear as it is one of the most important concept in biology.
Homologous features (“character”)–whether they be genes, mechanisms or morphologies–share an evolutionary history. That is, homologs share a character, from which they were derived, in an ancestor.The way the character looks (its “state”) is “primitive” if it looks like the ancestral character, and “derived” if it has changed from the ancestral state.
Orthologs and paralogs are both homologs, but have more specific meanings (i.e., are subsets of “homolog”)–both paralogs and orthologs are characters that share some evolutionary history. Orthologs (ortho=exact) have diverged because of a speciation event so that the history of the gene reflects the history of the species (in other words, this is the case where you are looking at the same exact gene in different organisms) (e.g., when a gene in one species, like Antp in Drosophila, diverges from the same gene in another species, like mab-5 in C. elegans).
Paralogs have diverged because of a gene duplication event (e.g., mab-5 and lin-39 are probably paralogs because they probably arose from a gene duplication event in an ancient ancestor or one can take the most popular among hox genes ,the one from Drosophila Ubx, abdA and AbdB are paralogs as they all arose from same parent gene through duplication). Paralogs will have different functions which may not be the case with orthologs.