The custom of blowing out birthday candles dates to ancient Greece

Ancient Greeks brought round honey cakes lit with candles to the temple of Artemis, goddess of the moon, to mimic the glow of moonlight. The smoke from blown-out candles was believed to carry prayers up to the gods. The tradition spread through Germany in the Middle Ages before becoming the global birthday ritual we know today.

Source: Plimpton, Ruth, 'Birthdays' / Historical anthropology records