Direct Grilling is the most basic and simple way to cook. Foods are cooked, or grilled, directly over the heat. What can be simpler than that? There is one basic variation to direct grilling, however: leaving the lid up, or keeping it down. Direct cooking is the oldest method of cooking. You can do it with a piece of meat, a stick and a fire. It is the direct exposure to the heat that cooks the food. In this day and age we have cooking devices with lids. It is this lid that determines whether the food is grilled or baked. By closing the lid you hold in the heat and allow foods to be cooked all over.
Imagine using a frying pan. The frying pan on the burner is using direct heat. The part of the food in direct contact with the pan is cooking. Now put the lid on that pan. The part of the food in direct contact with the pan is cooking faster, but the sides and top are also cooking because the lid is trapping the heat inside. The same principle applies to grilling. Open the lid and the rising heat will cook the bottom of the food. Close the lid and the trapped heat will cook the sides and top. Of course you still have to turn things over to get even cooking, but with the lid down you reduce the cooking time and cook through to the center faster than you would with the lid up.
The foods you cook with direct heat are the traditional grilling fare: steaks, burgers, fish fillets, etc. Anything that is less than 2 inches in thickness should be cooked by direct grilling. These are things that generally cook quickly and benefit from the fast cooking of a hot grill. As for having the lid up or down, generally you want to go with down. The only reason to grill with the lid up is for items that need a lot of basting, or cook so quickly that having the lid down increasing the risk of over cooking.
Any large food item or cuts of meat more than about 2 inches thick should be grilled indirectly.