There are a number of classifications schemes for explosives, but the U.S. Department of Justice Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) divides explosives into three categories based on the behavior of the material when unconfined:

Blasting Agents are high explosives that are less sensitive to initiation and cannot be detonated using a No. 8 strength blasting cap. These are also called “booster sensitive” or “noncap sensitive” explosives. They require a booster to detonate. The most common blasting agent is ANFO.
Low Explosives are an explosive material that deflagrates (or burns) at a high rate of speed when unconfined. The most common example is black powder.

High Explosives are highly sensitive explosives that when unconfined can be detonated using a No. 8 strength blasting cap. A high explosive detonation is accompanied by a shock wave moving through the explosive. Dynamite is a type of high explosive.