Coming in late to this but the Sunday before Christmas we got home after church and my 10 year old goes, "so pop, what does all of "this" (pointing to the tree and lights) have to do with Christmas."
So we sat down and read the 2 different parts of the bible where the birth of JC is covered. After that he goes, "uh, so yeah none of this has anything to do with Jesus then right?"
Me: Yup.
Son: So why do we do any of this?
Me: (and to answer the OP's question)
We really don't know when JC was born, but we've sorta decided that Christmas is the day we're going to celebrate his birthday. Now the gift giving is a perversion of the idea of good will and such. (I cited a few videos from "black friday", which I'd shown the kids previously. To which this same son goes, weren't these people just sitting with their families giving thanks for what they had?") WE give gifts to each other to remember God gave us JC as a gift so that we can be saved. What if I were to tell you the tree is part of a pagan religion?
Son: ....i'd ask why we have it up.
Me: Tradition? Honestly we probably shouldn't, but to make a long story short it's an adopted tradition from another religion. Thing is we don't celebrate that religion or the tree in such a way as it was used in that religion, it's just decoration in essence and doesn't really have any religions significance. It's like that picture frame. It's up all year long, but we don't pray to it, or worship it and unless we start dancing around the tree celebrating the solstice it's just that, a decoration. Just keep in mind the reason we have Christmas is to celebrate, even though there's no direction to do so, the birth of JC and we celebrate by giving gifts, as well as reflecting on the purpose of his life and death.
So that's the answer I gave my 3 kids to this very question. Made sense to them.
As a side note, after black friday and my kids watching some of the videos, particularly the one where the lady takes a vegitable steamer from a little girl, we as a family opted to find needy people and give them gifts. The kids were to find friends at school who "needed" things. For instance one son wanted to get shoes for his friend on his bball team who needed them badly. My daughter got her friend a jacket, cause "her mom said she could only afford to get her a sweater".
Christmas has been co opted by, surprise, corporations, it's literally that simple. Understand this and you can avoid many of the pitfalls and do your part to give charitably to those in need be you a Christian or not.
Christianity itself is only a soft monotheism anyway. "Trinity" 
