Answer: Christ's humiliation consisted in his being born, and that in a low condition, made under the law, undergoing the miseries of this life, the wrath of God, and the cursed death of the cross; in being buried, and continuing under the power of death for a time. (WSC)
The eternal Son of God humbled himself for his people's salvation. As Philippians 2:1-11 says, though he was God, equal with the Father, yet he became a servant, in humility counting others more significant than himself. He looked not only to his interests, but also to the interests of others.
As the catechism has already explained and as Philippians 2 recounts, his estate of humiliation began when he took on human nature, being conceived in Mary’s womb and born of her. And not only did the one by whom all things were created become man, but he was born into a relatively poor family. He had a manger for his cradle. He was an exile in Egypt as an infant. He grew up in an obscure little town as the son of a carpenter (Luke 2, Matt. 2). In addition, he submitted to the regulations of the Mosaic law such as circumcision as one of his people (Gal. 4:4, Luke 2:21-27).
While Jesus never sinned, yet he experienced the misery of our fallen estate. He was “a man of sorrows and acquainted with grief” (Is. 53:3). He bore our sins and received our punishment, undergoing the wrath of God and the painful, shameful, and cursed death of the cross (Is. 53). We see his experience of God’s wrath particularly as he approached his death in the Garden of Gethsemane (Luke 22:44) and on the cross itself (Matt. 27:46). Yet in both places he continued to call on his Father and submit to his will, entrusting his spirit and his vindication to his Father. Then, after Jesus died, his lifeless body was laid in the tomb and he continued in the state of the dead and under the dominion of death for a time (Rom. 6:9, Acts 2:24-27).
It is important to remember that Jesus undertook this work out of love for us and in willingly submission to his Father who sent him in love for us (Eph. 5:2, John 6:38). And while Jesus humbled himself during this time, yet this work was in fact a triumph. The cross - the epitome of shame and defeat - was actually the instrument by which our debt of sin was canceled and by which demonic powers were disarmed and put to shame (Col. 2:14-15). And it was because Jesus humbled himself in this way that he was consequently exalted in supreme glory as Lord and Savior (Phil. 2:9-11).