The reason why God became a man was to reconcile sinful man to Himself. The Bible says that we are all born in sin and separated from God; if we die in our sins, God will send us to hell. The Gospel (or good news) is that God the Son (Jesus) became a man, suffered and died on the cross for our sins and rose again on the third day.
If we will repent of our sins and put our faith and trust in Christ alone, then God will grant to us the gift of eternal life.
That's the good news of Christmas: a Savior is born (Jesus means "Savior")!
"And she will bring forth a Son, and you shall call His name Jesus, for He will save His people from their sins.” (Matthew 1:21)