A birthday cake is a cake served to a person on his or her birthday. A birthday cake is often decorated with small candles. Human tradition holds that the person with the birthday may make a wish, which will come true if all the candles can be blown out in one breath.
In 2376, Janeway had to search the databanks for hours on end, but eventually found Lieutenant CommanderTuvok's birthday, and replicated him a cake with a candle on it. He claimed that this was a Human tradition, and Vulcans do not "blow out candles." In the end, he blew it out, claiming that "it was a fire hazard." (VOY: "Fury")