Jesus’ birth date is simply unknown. The custom of celebrating December 25th as the birth date of Jesus (i.e. Christmas) did not arise until the third or fourth century. Prior to that time, there are reports of various Christian communities who celebrated Christmas once a year on every month of the calendar; and it was January 6th that was December 25th biggest competitor. For the Eastern Orthodox Church (Armenian), January 6th continues to be observed even though most societies today embrace December 25th.
Nevertheless, the significance seen in choosing this time period is symbolic. Why? Because there is symbolism found in the Winter Solstice that marks the end of darkening days and the beginning of lengthening light: a sign of renewal. Naturally, we would also expect to find this type of symbolism in other ancient religions. For those associated with the mystery religion of Mithras, this date meant the "Day of the Invincible Sun" (Dies Solis Invicti); for other religions, it was the Saturnalia (Dec. 17-24) and Brumalia (Dec. 25) which marked the "birthday of the unconquered Sun." In Christian communities, however, this day marked an appropriate day to observe the life of Jesus as "the light of the world" (John 8:12).
Though Christmas ultimately won out as a world wide observance, its success is largely due to the outreach of many friendly Christians. Unlike the mystery religions, mainline Christianity did not have secret initiatory rites (teletai), instead, it generally embraced any and all who showed an interest in the things of Jesus. Interestingly, this open arms approach is still prevalent today, a fact that is borne out by the sheer numbers who attend public Christmas observances near December 25th. Indeed, most Christians (admittedly with exception) encourage people of diverse ideologies to "come as you are" and reflect on the life and philosophies of Jesus in a public setting. Sources consulted: Ferm, An Encyclopedia of Religion, pg. 164-165. Cross, The Oxford Dictionary of the Christian Church, pg. 280. Metzger & Coogan, The Oxford Companion to the Bible, pg. 112. Freke & Gandy, Was The Original Jesus A Pagan God? pg. 34. Metzger, NT, pg. 103. Mercatante, The Facts On File Encyclopedia of World Mythology and Legend, pg. 175-177.