As a person who was raised without religion, but who loves Christmas, I view the Christmas season as a time to connect with family and friends. Sort of a closure to the season, which begins at Thanksgiving.
The present buying may be commercial, but I certainly spend a lot of time thinking about friends and family, some who I don't see a whole lot during the year, as I try to find a gift they would truly like. This year I tried to include my son, asking him what his great grandmother would like, his aunt, his uncle. Writing cards to family, also something you can have a young child help with, my son colors/draws a picture on each card as we talk about the person we are sending them to. Christmas is about connecting again with my larger family, and finally on Christmas morning with our immediate family.
We also take every opportunity during the season to help others...buying the Christmas tree from a lot that supports a charity we care about, my 2 year old pick out a toy and took it to the fire station to donate to toys for tots, I always pick out a charity to donate to. And this year, I have tried hard to include my son in all these activities, so he can appreciate how much we have and how lucky we are.
As for books, I always loved the night before christmas, and my son loved that one this year, but there are tons of non-religious christmas books out there. Many focus again on connecting with family and friends. He also watched the old Rudolph movie and loved it.
As for the tree, I don't think you need to explain why it is there. It is fun. It is about spending the time together picking it out, putting it up and decorating it. In a busy world filled with tv, computer, ipods, etc., it is a wonderful activity that slows the world down a bit and brings the family together for a common and fun activity. Not to mention the ornaments can bring back so many memories and start up great conversations.