Isa 7:14 Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.
Immanuel means "God with us". The Son of God had come to dwell with, or tabernacle on earth with His people.
John 1:14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
The Feast of Tabernacles (Sukkot), occurs five days after the Day of Atonement, and is a festival of rejoicing and celebration of deliverance from slavery in Egypt (Leviticus 23:42-43).
Luke 2:7 And she brought forth her firstborn son, and wrapped him in swaddling clothes, and laid him in a manger; because there was no room for them in the inn.
Luke 2:8 And there were in the same country shepherds abiding in the field, keeping watch over their flock by night.
Luke 2:9 And, lo, the angel of the Lord came upon them, and the glory of the Lord shone round about them: and they were sore afraid.
Luke 2:10 And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people.
Luke 2:11 For unto you is born this day in the city of David a Saviour, which is Christ the Lord.
Why was there no room at the inn? Bethlehem is only about 5 miles from Jerusalem, and all the men of Israel had come to the Temple in Jerusalem to attend the festival of Booths/Ingathering/Tabernacles as required by the law of Moses (Exo. 23:14-17, 34:22-23, Deut 16:16). Every room for miles around Jerusalem would have been already taken by pilgrims, so all that Mary and Joseph could find for shelter was a stable. During Tabernacles, everyone was to live in temporary booths (Sukkot), as a memorial to Israel's pilgrimage out of Egypt - Lev. 23:42-43. The birth of the Savior, in what amounted to a temporary dwelling rather than a house, signaled the coming deliverance of God's people from slavery to sin, and their departing for the promised land, which is symbolized by Tabernacles.
Also of note is the fact that the Feast of Tabernacles is an eight day feast (Lev 23:36, 39). Why eight days? It may be because an infant was dedicated to God by performing circumcision on the eighth day after birth:
Luke 2:21 And when eight days were accomplished for the circumcising of the child, his name was called Yeshua, which was so named of the angel before he was conceived in the womb.
So the infant Yeshua would have been circumcised on the eighth and last day of the Feast of Tabernacles, a Sabbath day. The Jews today consider this a separate festival from Tabernacles, and they call it Shemini Atzeret.