This term means similar (homoi) nature (ousious), in contrast to same (homoousios) or different (heteroousios) nature.  At the Council of Nicea, moderates suggested the term as a compromise between the homoousios of Athanasius and heteroousios) of Arius. Homoousios was chosen because it correctly defends that the Father and Son both share the same divine nature (John 1:1).