It's the day the wise men showed up to see baby Jesus. In some cultures its the more secular part of the holiday- gif t giving, whereas Christmas would be more about the mass at church.
The gifts from the magi are kind of like a cross between Easter and Christmas stockings. You collect grass and put it in your shoes and leave them by the front door (instead of a basket for the Easter bunny). The wise men come and let their camels eat the grass. Then they leave candy and little presents in the shoes.
Three Kings Day is also known as "Epiphany." It's when the magi visit the baby Jesus.
We actually don't do too much with it - we take down our tree, and the church service (Episcopal) this morning had a cute procession where the kids followed the star to baby Jesus in the manger, and then some rather large kings from orient joined the procession.
(My friend is from spain and it's a bigger day at her house - they bake bread that is shaped like a crown and get small gifts in the morning).