That is quite interesting.
Well, truth is, Christmas tradition have changed in the last decades. But on January 6th, it is the Reyes Magos (Wizard Kings) celebration, the epifanía, which is the moment where the Wise Men offered their gifts to baby Jesus. In that spirit, that day the Reyes Magos bring presents to the children. The night between 5 and 6of January, children put on the table a dish with some grass and a glass of water "for the camels". And they left their shoes in the living-room. The following morning the grass and water is gone and there are gifts on their shoes!
Well, traditionally we had some exchange of not so important gifts on Christmas, for adults and children, and on January 6th the children got their main gifts. Empirically, often on Christmas children got something like clothing or something they really needed, and the Reyes gave them toys, books and things to truly enjoy.
But in the last decades there has been a change. On Christmas' Day comes Santa (we called him Papá Noel) who brings presents to the children. We still have the Reyes Magos on January 6th, but they are less important now. The main even is shifting towards Christmas and Papá Noel.
Also, in some of our provinces, particularly on the North, it was Baby Jesus who brought presents on Christmas' Day, but that is also being replaced by Papá Noel.
Christmas has always been the main religious celebration here, and we put a Pesebre, the small figurines representing the Virgin Mary, Joseph and baby Jesus in the barn, with the shepherds, the Reyes Magos and all that. But lately it becomes much more commercial, and many families did not even put the Pesebre. There is also more people that does not do anything religious related, just buys gifts for the Children and put the Tree because it is fun.
I never believed in Papá Noel, first because I am old and he was not so important, but also because Christmas' Day is my birthday, so everyone brought me gifts without pretendind they came from someone else. But I loved the Reyes! Some of my best memories are from waking up on January 6th.