When the Son of God became human and was born, he was honouring or fulfilling the terms of an agreement made in heaven within the Trinity. It is not possible for us to probe too far into that agreement, although we can see that each person of the Trinity had roles to fulfil in the provision of salvation for sinners. As far as the Son was concerned, his role was to become a man, and we know from other Bible passages that the Father and the Spirit were involved.
When we think of him becoming a real man, we should remind ourselves that he came as the servant of the Father and as the representative of his people. He had to live a completely holy life, and that holy life included his conception and birth, in order for that life to be reckoned to his people as their righteousness.
The infant who was lying in the manger would yet find himself on the cross, paying the penalty that God demanded for the sins of his people. Later still, he would be raised from the dead and would ascend to heaven as the forerunner of his people, ensuring that they all would yet reach the new heavens and new earth.
Timewise, we have moved a long way from the manger, yet we should not forget that the Son of God came there to honour an eternal agreement, and he is still honouring it now as the One enthroned on high.
Having contemplated his birth, how should we feel? Several answers could be given, but three details can be mentioned. We should be humble, hopeful and happy. The great God of eternity became man for us, and that should make us humble. The great God of eternity became man for us with a great plan of deliverance, and that should make us hopeful. The great God of eternity became man in order to be with us, and not only in this life, and that should make us happy.