Apollinarianism was the heresy taught by Apollinaris the Younger, bishop of Laodicea in Syria about 361. He taught that the Logos of God, which became the divine nature of Christ, took the place of the rational human soul of Jesus and that the body of Christ was a glorified form of human nature. In other words, though Jesus was a man, He did not have a human mind but that the mind of Christ was solely divine. Apollinaris taught that the two natures of Christ could not coexist within one person. His solution was to lessen the human nature of Christ.
Apollinarianism was condemned by the Second General Council at Constantinople in 381. This heresy denies the true and complete humanity in the person of Jesus which in turn, can jeopardize the value of the atonement since Jesus is declared to be both God and man to atone. He needed to be God to offer a pure and holy sacrifice of sufficient value and He needed to be a man in order to die for men.
Jesus is completely both God and man. This is known as the Hypostatic Union.

*

"In the beginning was the Word, and the Word was with God, and the Word was God...and the Word became flesh and dwelt among us..." (John 1:1,14).
*

"for Him dwells all the fullness of deity in bodily form," (Col. 2:9).