It's Greek, and means, "of the same substance". This is not to be confused with homoiousios, which means "of differing (or similar) substance"; Both are theological concepts, the former being a stance held by the theologian Athanasius, and the latter being heralded by the theologian Arius.

Specifically, the differences between an Athanasian and an Arian view point are the 'how' and then 'when' of Jesus' existence. The Athanasian concept of homoousios means that the Son was "begotten" and has existed all along. This turned into quite a controversy, the focus of which centered on whether or not Jesus was "of the same substance" as the Godhead, and if he was "created" by the Godhead. While this does not seem to have much of an implication to the casual reader or believer, it has great weight, concerning the church's prevailing beliefs as to the structure and weight of the Trinity.

Belief in the concept of "homoousios" was the position later adopted by the Church. Arius found himself in the unfortunate position of being exiled shortly thereafter.