Hypostasis had come into use as a technical term prior to the Christological debates of the late fourth and fifth centuries. Before there were Christians, the word was used in Greek philosophy, primarily in Stoicism. Hypostasis had some use in the New Testament that reflect the later, technical understanding of the word; especially Hebrews 1:3. Although it can be rendered literally as "substance" this has been a cause of some confusion so it is now often translated "subsistence". It denotes an actual, concrete existence, in contrast with abstract categories such as Platonic ideals.
The First Council of Nicaea declared that the Father and the Son are of the same substance and are co-eternal. This belief was expressed in the Nicene Creed.
Read more about this topic: Hypostatic Union