This is a time that people who believe in Jesus have designated to celebrate His birth (even though, yes, He was probably born in the springtime, and yes, this time was only selected to compete with pagan Winter Solstice festivals). To fully appreciate the meaning of Christmas, you must understand what a huge problem to humanity sin is, and what a vast chasm God traversed to be incarnated and defeat sin for us.
By giving each other gifts, Christians commemorate the gifts that the middle-eastern magi gave to the infant messiah, and, more importantly, the gift to the human race that Jesus was, and is.
Without the incarnation of God, no man would have ever lived a sinless life; without a sinless man, there never would have been a propitiation for sin; without propitiation, we would all be lost in our sins and we would have no relationship with God; without a relationship with God, life is temporal, death is fearsome, and virtue is one-dimensional.
Fortunately, the incarnation did happen, and we can have a relationship with God, because He chose to have a relationship with us. He came to walk among us, speak with us - be with us. Emmanuel: God with us.
The power of Christmas need not be entirely lost on those who do not believe. This is a time of generosity for the generous, a time of peace for the peaceful, a time to be with and honor your family. If you are estranged from your loved ones, please reconnect with them today: make the phone call you've been putting off. If you are embattled in a grudge with your neighbor (or any person), please use today to reconcile. If you've been blessed with more than you need, please give of your abundance to those struck with tragedy.