A sweet tooth is a taste for sweet, sugary foods. Someone with a sweet tooth is likely to have a cinnamon roll for breakfast instead of an omelet.
Most people who profess to having a sweet tooth are big fans of dessert. The phrase has been used in English for hundreds of years, since the late fourteenth century, and it comes from toothsome, an even older word meaning "delicious or tasty." This sense of tooth standing in for taste gave rise to sweet tooth, or "particularly enjoying sweet tastes."