HOW DO PEOPLE WALK ON FIRE?

It is true that the temperature of the coals is over 1000 degrees F (535 degrees C), and that human flesh burns at much lower temperatures, but temperature isn't the only part of the relevant physics. Different substances have different heat capacities. Water is the standard. Our feet are mostly water. The coals have a much lower heat capacity than water. That means that the same 

amount of energy flowing away from the coals will lower their temperature much more than that same energy flowing to the feet will raise the foot's temperature. If the foot stays in contact with the coals, energy will keep flowing until they both reach the same temperature. However, this takes time, and how much depends on the heat conductivity. There are good heat conductors, like water, and poor conductors/heat insulators, such as ash. The feet cool down the local area of the coals they touch, and it takes time for energy to flow from the rest of the fire to the cool spot. You can sometimes see dull orange footprints in the coals right after someone walks. Water is a good heat conductor and energy transferred to the foot is rapidly conducted away from the contact points so the temperature doesn't rise to the burning point. Temperature, heat capacity, and thermal conductivity are all important in this demonstration.

A more familiar experience which involves the same physics is baking brownies in the oven set to 450 degrees F. Everything in the oven is 450 degrees, but you don't fear putting your hand in the oven air. The air has a very low heat capacity meaning it stores very little thermal energy. Air is also a heat insulator. Your hand (mostly water) cools the air locally and heats up very little. If you stick your finger in the brownie, you might get burned. It is mostly water like your hand and has a pretty good heat conductivity. Thermal energy will flow to your finger raising its temperature quickly. The metal pan is another matter. It has a high heat capacity and a high conductivity. Touch it without a potholder and you might instantly burn your fingers.

What the physics tells you, is that if you walk fast and don't stay in contact with the coals very long, you won't get badly burned.

Here is a further expatiation by the Myth Busters.