In France, we eat a "galette", a round shaped puff pastry cake filled with almonds + sugar + butter filling or a "royaume" (kingdom) crown shaped bun with candied fruit and sugar on top . There's a trinket inside called "fève" because a long time ago, it was a real fava bean. When the cake is cut, the youngest child goes under the table and is asked "who's this piece for?" he says someone's name and so on. The one who finds the trinket hidden in his/her piece puts on the cardboard crown that the baker gives along with the cake, s/he's the King or the Queen of the day and usually, s/he's to buy another cake that will be shared and the one who finds the trinket etc etc. When someone gets the trinket for the second time, one who hasn't gotten it yet decides to be the next one to buy the cake. This can last till the end of January... just in time to switch to eating crêpes on Candelmass day! You can see what it looks like and the recipe here Epiphany
In Spain, it's when the Kings bring the kids their Christmas gifts. They also have a crown shaped bun called "roscón de reyes"