Convective and evaporative cooling. Even though your breath is warmer than room air, it’s cooler than the food, plus it entrains surrounding room air which is even cooler and drier, via the Venturi principle. So the layer of warm air adjacent to the hot food is replaced by air at a lower temperature (convective cooling) and containing lower humidity (improving evaporative cooling).
It’s more effective to blow on just a forkful or spoonful of food prior to entering the mouth than it is to try to cool the entire mass of hot food on the plate or in the bowl.