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For more on marking an answer as the "Best Answer", please visit our FAQ.Blowing on hot food does cool it down because your breath is cooler than the food, and you are ventilating it -- you are moving hot air away and replacing it with cooler air.
However, a large part of the effect is that it increases evaporation of water in the food, by removing damp air and replacing it with drier. You can easily demonstrate this. Lick the back of one hand, then blow on the back of each hand -- which feels cooler? In that case your breath is probably actually warmer than your hand.
Evaporation cools efficiently because the water is changing from a liquid to a gas, and the latent heat of evaporation sucks extra heat from the food. It's why we sweat, and also how fridges and air-conditioners work. It's also why scalds from steam are worse than those from the same mass of liquid water at the same temperature -- in that case the latent heat of evaporation is dumped into your skin. In fact the same thing happens a bit when you blow on cold hands -- you'll notice that your hands get damper.
If hot food is dry, or if the water is not exposed to the air, blowing will be much less effective, as evaporation is not involved. This is why it's so easy to scald yourself when drinking those soups which have a little oil on the top -- they can't lose heat by steaming. Likewise, a cup of tea will stay hot much longer with a lid on it.