As a child, our King Cake was served on Epiphany, the last of the 12 Days of Christmas. Epiphany celebrates the three kings or wise men visiting the baby Jesus, so a cake named after these kings seems apropos. If my mom would remember, she'd wrap a coin or dried bean in foil and bake it into the cake.
Nowadays, a king cake is more aligned with Mardi Gras, AKA Fat Tuesday, the day before Lent begins. It's actually OK to serve a king cake recipe anytime from Epiphany through Mardi Gras. King cakes are found in grocery stores across the states, made of eggy brioche dough or even puff pastry, and filled with cream cheese, cinnamon sugar, fruit, or chocolate.