What is direct heat?
Direct vs. Indirect Heat are terms usually used when referring to American style BBQing or grilling. While the terms can apply to other areas of cooking as well their usefulness makes the most sense in this context.

Direct Heat

A method of heat transfer in which heat waves radiate from a source (for example, an open burner or grill) and travel directly to the item being heated with no conductor between heat source and food. Examples are grilling, broiling, barbecueing, and toasting. (source)

Keep in mind that the grill itself doesn't really act as a conductor as much as a way to hold the food in a static position relative to the heat source. To better understand direct heat, understand it's complement:

Indirect Heat

When using indirect heat, your goal is to never have any part of the meat directly over flames or charcoal. You can only do indirect cooking with a charcoal or gas grill that has a cover. In this respect, it acts very much like a convection oven... the heat swirls around the inside of the grill and the meat is cooked from all angles. This also eliminates the need to 'flip' or turn your meat during the cooking process. (source)

This is generally used to cook large pieces of heat that need a long time to cook. A smoker is an example of the kind of equipment used to cook with indirect heat.