[Greek homos, same.]
Things that are homogeneous are of the same kind or alike; to homogenize something is to make all its parts uniform or similar (as in bringing the fat droplets in milk to a common small size so it emulsifies); things that are homocentric have the same centre (but see the next entry); those that are homologous (Greek logos, ratio or proportion) are of the same essential nature.
Someone homosexual is sexually attracted to a person of her or her own sex (as opposed to heterosexual, see hetero-). The link between homo- and homosexuality is sufficiently strong that in a few terms the prefix relates specifically to it: homoerotic, concerning or arousing sexual desire centred on a person of the same sex; and homophobia, an irrational aversion to homosexuality and homosexuals.
This and the sense explained in the next entry are sometimes confused.