What does incarnate mean? How was Jesus God incarnate?

The Latin verb incarnare meant "to make flesh." When we say that Jesus
Christ is God "Incarnate," we mean that the Son of God took on a
fleshly, bodily form (John 1:14). However, when this happened in the
womb of Mary, Jesus' earthly mother, He did not stop being deity.
Although Jesus became fully human (Hebrews 2:17), He retained His
status as God (John 1:1, 14). How Jesus is able to be both man and God
simultaneously is one of the great mysteries of Christianity but is
nevertheless a test of orthodoxy (1 John 4:2; 2 John 1:7). Jesus has
two distinct natures, divine and human. "Believe me when I say that I
am in the Father and the Father is in me" (John 14:11).

The Bible clearly teaches the deity of Christ by presenting His
fulfillment of numerous Old Testament prophecies (Isaiah 7:14; Psalm
2:7), His eternal existence (John 1:1–3; John 8:58), His miraculous
virgin birth (Luke 1:26–31), His miracles (Matthew 9:24–25), His
authority to forgive sin (Matthew 9:6), His acceptance of worship
(Matthew 14:33), His ability to predict the future (Matthew 24:1–2),
and His resurrection from the dead (Luke 24:36–39). The writer of
Hebrews tells us Jesus is superior to angels (Hebrews 1:4–5) and
angels are to worship Him (Hebrews 1:6).

The Bible also teaches the Incarnation—Jesus became fully human by
taking on human flesh. Jesus was conceived in the womb and was born
(Luke 2:7), He experienced normal aging (Luke 2:40), He had natural
physical needs (John 19:28) and human emotions (Matthew 26:38), He
learned (Luke 2:52), He died a physical death (Luke 23:46), and He was
resurrected with a physical body (Luke 24:39). Jesus was human in
every way except for sin; He lived a completely sinless life (Hebrews
4:15).

When Christ took on the form of a human, His nature did not change,
but His position did. Jesus, in His original nature of God in spirit
form, humbled Himself by laying aside His glory and privileges
(Philippians 2:6–8). God can never stop being God because He is
immutable (Hebrews 13:8) and infinite (Revelation 1:8). If Jesus
stopped being fully God for even a split second, all life would die
(see Acts 17:28). The doctrine of the Incarnation says that Jesus,
while remaining fully God, became fully man.