To mark how old you are … the older you get the more likely it is to see your cake from 3 houses down. And in case you ever forgot how old you were, you have a yummy cake to smile up at you and say, “You’re old!”
I looked for some more in depth answers, rather than what I initially came up with on a search, but didn’t find much. The first, History Of Cakes gives a short answer, but doesn’t appear to be biased:
And I did find quite a few sites pointing to Artemis and the Greeks. Most of those sites were warnings about avoiding Pagan Birthdays, but the above site did give a reference. Most of the sites I visited associated lighting candles with prayer, mentioning the Romans and Saturnalia, Artemis, etc. Looks like we just substituted wishes for prayers. If you scroll to the section on birthday cakes in the first link, it gives a pretty good summation of the information from a lot of the other sites I found, discussing the origin of birthday cakes.