The traditional religious "message" of Christmas has been a celebration of the birth of Christ, who, according to Christians, came into the world to redeem mankind from its sins. The more recent "message" behind Christmas has emphasized the exchange of gifts as part of a yearly ritual of affection among loved ones. The emphasis here has been on the celebration of close ties among family and friends; greetings are given to communicate feelings of fellowship and goodwill. Unfortunately, Christmas has become more and more commercialized over the years, although most people still try to keep the second traditional reason for its celebration in mind, even if they neglect the first.
As post 2 has explained, Christmas is the celebration of the birth of Christ, but we do not actually know when this birth occurred. Historically, the Catholic Church selected December to celebrate because they were trying to ease the transition for pagans. The pagans celebrated Winter Solstice and the evergreen tree was a big part of this celebration. The Catholic church adopted the tree and the time of year for the celebration. Now days, many non-Christians celebrate Christmas as time of good will and gift giving rather than the celebration of Christ's birth. For some, Christmas has become a cultural rather than a spiritual celebration.
This is a broad question and can be answered in many ways. From a more traditional and religious point of view, Christmas is about the celebration of the birth of Christ. To be sure, from a historical point of view, no one knows the date of the birth of Christ, but the church celebrates it on that day - December 25th. So, in light of this, for many people around the world, Christmas is preeminently a religious holiday that remembers the birth of a savior. The gospels of Matthew and Luke have the birth narratives of Christ.
For others, Christmas is more of a secular holiday, where people wish each other well and even give gifts to those they love. For these people it is a day of good will towards others.