Kevin DeYoung: (original source but never fully contained within, the human nature.
The term was originally a pejorative label given by Lutheran theologians in their debates with Reformed divines over the real presence of Christ in the Lord’s Supper. Whereas Lutherans affirmed the physical presence of Christ’s body in, with, and under the elements, Reformed theologians spoke of a real spiritual presence. In order to maintain their position (later termed consubstantiation), Lutherans argued that the attribute of omnipresence should be predicated not just of Christ’s divine nature, but also of his human nature.
Reformed theologians, by contrast, held to a different understanding of the communicatio idiomatum (communion of properties), insisting that what can be said about either nature can be said about the Person of the Son, but cannot be automatically predicated to the other nature. Consequently, the divine Logos is omnipresent, but Christ’s human body is not. In other words, the Son, even in his incarnate state, is able to live a divine life outside (extra) his human nature. Or as the Heidelberg Catechism puts it: “Since divinity is not limited and is present everywhere, it is evident that Christ’s divinity is surely beyond the bounds of the humanity he has taken on, but at the same time his divinity is in and remains personally united to his humanity” (Q/A 48).
While the doctrine may seem like unnecessary and overly precise doctrinal wrangling, the extra Calvinisticum is crucial for protecting a classic understanding of the incarnation. In fact, some have preferred the term extra Catholicum because even though the doctrine is attributed to John Calvin, it was clearly the position of church fathers like Augustine, Cyril, and Athanasius, and was taught throughout the Middle Ages. The extra is an important doctrine in that it safeguards the transcendence of Christ’s divine nature (i.e., it cannot be contained) and the genuineness of the human nature (i.e., it does not possess attributes reserved for divinity).
The extra also reminds us that in the incarnation “the Son did not cease to be what he had always been” (Wellum, God the Son Incarnate, 332). He continued to sustain the universe (Col. 1:15-17; Heb. 1:1-3) and to exercise his divine attributes together with the Father and the Spirit. When Mary conceived a child by the power of the Holy Spirit, the divine nature did not undergo any essential change. Better to say the Person of the Son became incarnate than to say the divine nature took on human flesh (for the latter suggests the divine nature changed in its essential properties).
All this means–because the divine nature did not undergo essential change–that in coming to earth, the Son of God did not abdicate his rule, but extended it. It also means–because the human nature was not swallowed up by the divine–that the Son’s earthly obedience was free and voluntary. In short, the extra protects a Chalcedonian understanding of the incarnation that Christ’s divine and human natures were indissolubly joined, yet “without confusion” and “without change.”