Some notes to the origin (because it seems no answer mentions it):
In the bible, among the first people to see the newborn Jesus, there were three foreign scholars/kings/...?, commonly called Caspar, Melchior and Balthasar. Before Jesus was born, they heard a propecy about him, startet to travel to see him, and were led to the place were he was born by a moving star (see the 4. person in LectorHectors answer, symbolizing the star).
They also brought presents: (among other things?) there were gold, incense and myrrhe (all three pretty valuable back then).
...
Today, eg. in Austria, groups of children "travel" around on 06.01., usually organized by the local priest, and often with king customescostumes. That they sing christmas songs, write on house doors (if the owner allows it) etc. is sufficiently covered by others, but some of them even now give out incense for home usage.
Nowadays, the whole action of course is connected with charity; many people donate money (where it goes depends on the location). (And the children usually get quite a few sweets too).