In classical Roman culture, 'cakes' of flat rounds made with flour containing nuts, leavened with yeast, and sweetened with honey were occasionally served at special birthdays, but more often at weddings as in Ancient Greece.

In early Europe, the words for cake and bread were virtually interchangeable; the only difference being that cakes were sweet while bread was not. In the 15th century, bakeries in Germany conceived the idea of marketing one-layer cakes for customers' birthdays and not only for their weddings, and thus the modern birthday cake was born. During the 17th century, the birthday cake took on more or less its contemporary form. However, these elaborate cakes, which possessed many aspects of contemporary cakes (such as multiple layers, icing, and decorations), were only available to the very wealthy. Birthday cakes became more and more proletarianized as a result of the industrial revolution, as materials and tools became more advanced and more accessible.

The addition of such decorations as candles, wording, etc. are attributed to Western Europe and the United States.

More Info: en.wikipedia.org