The ancient Egyptians are credited with “inventing” the celebration of birthdays. They believed when pharaohs were crowned, they became gods, so their coronation day was a pretty big deal. That was their “birth” as a god.
Ancient Greeks borrowed the tradition but rightfully realized that a dessert would make the celebration all the more meaningful. So they baked moon-shaped cakes to offer up to Artemis, goddess of the moon, as a tribute. They decorated them with lit candles to make the cakes shine like the moon. Hence, the reason we light our birthday cakes on fire.