Dry-frying uses infrared radiation and hot air. It comprises the use of an oven, grill or an air fryer. Often the fat already present in the food is sufficient to provide for a nice roasting of the surface. And this without the food getting charred.
Examples are meats, fish, cheese, or pre-fried French fries. In the example when we want to peel a pepper the high oven temperature will cause the pepper surface to get slightly charred. This helps to remove the peel.
Another example of dry-frying is grilling, either in an oven, on a wood fire or on a barbeque. When a wood fire is used (and to a lesser extent on a barbeque) the food is also smoked at the same time. Thus providing a smoky taste. In general, since air is not a good conductor of heat at all, dry-frying times may be longer than for example frying in oil. Unless we apply very high temperatures.
Air-fryers have gained in popularity primarily since they promote to be a more healthy way of food preparation. Actually air-fryers do compare with deep-fryers in oil. Deep-frying in oil indeed does cause the food products to take up oil. However, all pre-fried (pre-cooked) foods such as french fries do contain already so much oil that they can be easily air-fried and display a similar color, smell and taste. And the formation of carcinogens such as acrylamide at the surface of the potatoes will still occur in air-fryers.