Ousia (Οὐσία) is the Ancient Greek noun formed on the feminine present participle of εἶναι (to be); it is analogous to the English participle being, and the Greek ontic. Ousia is often translated (sometimes incorrectly) to Latin as substantia and essentia, and to English as substance and essence; and (loosely) also as (contextually) the Latin word accident —  which conflicts with the denotation of sumbebekos, given that Aristotle uses sumbebekos in showing that inhuman things (objects) also are substantive. 
Philosophic and scientific use
The Greek philosophers Plato and Aristotle used ousia in their philosophies; their denotations are the contemporary philosophic and theologic usages. Aristotle used ousia in creating animal phyla in biology, and hypostasis denoting general existence (reality), and ousia denoting a specific substance, essence, being, person, or thing.
Later, Martin Heidegger said that the original meaning of the word ousia was lost in its translation to the Latin, and, subsequently, in its translation to modern languages. For him, ousia means Being, not substance, that is, not some thing or some being that "stood"(-stance) "under"(sub-). Moreover, he also uses the bi-nomial parousia-apousia, denoting presence-absence, and hypostasis denoting existence.
Early religious significance
Origen, (c.182–c.251) used ousia in defining God as one genus of ousia, while being three, distinct species of hypostasis: the Father, the Son, and the Holy Spirit. The Synods of Antioch condemned the word homoousios (same substance) because it originated in pagan Greek philosophy. The Paul of Samosata entry of the Catholic Encyclopedia says: 
- It must be regarded as certain that the council, which condemned Paul, rejected the term homoousios; but, naturally, only in a false sense, used by Paul; not, it seems, because he meant by it a unity of Hypostasis in the Trinity (so St. Hilary), but because he intended, by it, a common substance, out of which both Father and Son proceeded, or which it divided between them — so St. Basil and St. Athanasius; but the question is not clear. The objectors to the Nicene doctrine in the fourth century made copious use of this disapproval of the Nicene word by a famous council.
The general agreed upon meaning of ousia in Eastern Christianity is all that subsist by itself and which has not its being in another. In contrast to hypostasis which is used to mean reality or existence.
Christian debate about Homoousios and Homoiousios
In A.D. 325, the First Council of Nicaea
debated the denotations of the Greek words homoousios
(same substance) and homoiousios
(similar substance). To wit, they affirmed that the Father, the Son, and the Holy Spirit (the Godhead
) all are of the same substance, being or essence. Edward Gibbon noted that the First Council of Nicaea's semantic controversy was a quibble about iota
(i), the smallest Greek letter. Moreover, the Chalcedonian Creed
of A.D. 451 says that God is one ousia
, yet three hypostases