If you increase the temperature you will increase the rate at which the coal will burn. If you increase the concentration of oxygen in the air you will increase the rate at which the coal will burn. A match is a very small piece of wood. Will start burning much faster than a log. Kindling is a small piece of wood and will burn faster than a large log.
Air contains oxygen.
Blowing air across the fire increases the oxygen concentration in that place. The loosely stacked wood pile allows for oxygen to freely flow into the fire. A catalyst is a chemical that increases the speed or rate of a chemical reaction without undergoing permanent chemical change. The catalyst lowers the energy necessary to get a reaction started. These are surface or contact catalysts.