To broil is to cook something with direct exposure to fire. Broiling is similar to grilling, but you can also oven broil your steak if it's raining out.
Have you ever had a cookout? If so, someone was probably heating up hamburgers and hot dogs on the grill. This is a type of broiling. Broiling involves direct exposure to a flame. You can broil with a grill, a campfire, and with many types of stoves. You can also say that cooking by broiling is a broil (the noun). People like to get a broil going, especially in the summer.