What does it mean to say, "It's the birth date of the messiah?"
What is messiah?
From a history of religions perspective, it's the idea that a Redeemer for the world came into existence in accordance with the prophecy of the biblical prophet Isaiah in Isaiah 11.
Christians believe that the messianic mission will be fulfilled in a Second Coming. Jews believe it has not yet been fulfilled. From a history of religions perspective, there is a huge gap between these aspects of Judaism and Christianity. Indeed, the differences have led to many deaths and even wars.
But let's look at it differently. What does Christmas represent? We humans possess an internal need for a meaning to our lives, for life to have purpose, for a telos in philosophical terms. We don't want to just exist. We want to exist for a reason, something that has greater significance than mere biological survival.
In religious terms, that idea is expressed in the concept of Redemption: that God will send a figure, a person, to return the world to the original bliss that God intended in the Garden of Eden. So Redemption expresses a Paradisal vision to fulfill the meaning of life: return to the Garden.
But on a less cosmic level, we all seek a personal redemption, particularly in a secularized world in which Ultimate Purpose given by a Divine Force may not exist. Instead, all human beings seek a reason for our personal existence beyond mere physical survival of the self.
In both Christianity and Judaism, this ideal is expressed in the concept of Redemption, and a personal or national Redeemer. But Redemption does not require a single person. It might simply be personal.
Reform Judaism theorized a Messianic time: a time brought about through human action in which we live as though we live in the Garden. It's a time of peace and human acceptance: a Garden without the garden.
Therefore Christmas, and the idea of Christ, a messiah, expresses a human aspiration thatJudaism fulfills at Passover and Christianity at Easter: not a Messianic Redemption necessarily, a personal messiah, but the fulfillment of human freedom under the law of God who reigns over the world and accepts all humans equally. This paradisal vision does not separate religions. It unites us all in the Vision of the aspirational world in which "every person shall live under their vine and under their fig tree, and none shall make them afraid." (Micah 4:4)