A breath is a special power that a dragon has. Each breed of dragon has a different type of breath, as well as a different element. The element of the breath corresponds with the dragon's element.
The fire from the dragons mouth has always been a mystery. Some says that the dragons have a special gass in their stomac, witch eventually becomes fire as the dragon breathe. But the most likely theory is that the dragons have a "spark pocket" in their mouth. If the dragon rub its teeth against each other, a spark will appear from the spark pocket and become fire.