Hypostatic union (from the Greek: ὑπόστασις, "hypostasis," translated reality or person) is a technical term in Christian theology employed in mainstream Christology to describe the presence of both human and divine natures in Jesus Christ. It became official at the Council of Chalcedon, which stated that the two natures (divine and human) are united in the one person (existence or reality, "hypostasis") of Christ.
The First Council of Nicaea defined the Trinity as being three persons or realities (hypostases) with one essence (ousia).
Theodore of Mopsuestia went in the other direction, arguing that in Christ there were two natures (human and divine) and two hypostases (in the sense of "essence" or "person") that co-existed.
The Chalcedonian Creed agreed with Theodore that there were two natures in the Incarnation. However, the Council of Chalcedon also insisted that hypostasis be used as it was in the Trinitarian definition: to indicate the person and not the nature as with Apollinarius.
Thus, the Council declared that in Christ there are two natures; each retaining its own properties, and together united in one subsistence and in one single person (εἰς ἓν πρόσωπον καὶ μίαν ὑπόστασιν, eis hen prosopon kai mian hupostasin)
As the precise nature of this union is held to defy finite human comprehension, the hypostatic union is also referred to by the alternative term "mystical union."
Those who rejected the Chalcedonian Creed were known as Monophysites because they would only accept a definition that characterized the incarnate Son as having one nature. The Chalcedonian acceptance of the hypostatic union was described by these persons as a dyophysite Christology, from the Greek for "two natures."