There are two methods to grill food over a gas, wood, charcoal, or infrared - direct or indirect cooking. Using the direct heat method, the food item is placed directly over the flame or coals. This method exposes the food item to very hot temperatures, often in excess of 500F or 900F for infrared grills. This is the fastest way to cook food items on a grill. The food items are cooked by the flames and radiant heat coming from the heat source of the grill. The direct heat method is used for grilling steaks, hamburgers, hot dogs, sausage, pork chops and skewers. The food items must be carefully monitored and turned frequently so as to not burn them.
Using indirect heat, you place the food item so that it is not directly over flames or coals. This is done by having the fire or coals on only one section of the grill and placing the food item on a part of the cooking grill opposite the flames or coals - for example, having the burners going on the right side of a gas grill but off on the left side or placing the coals on the right side of the grill and no coals on the left side. In a charcoal grill, when indirect grilling it is best to place a foil pan of water under the food to keep it from drying out. Using the indirect grilling method is best for large cuts of meat or bone-in poultry. It allows the food to cook all the way through without burning or charring on the outside of the meat.
On the Big Green Egg there is a plate setter insert (pictured here) that you place under the grill rack to facilitate indirect cooking, no BGEggHead should be without one! Other examples of items that are used for indirect cooking on the BGE include Baking Stones (also pictured here).
Sources: http://en.wikipedia.org/wiki/Grilling & Photo copied off Google Image site