Mmmm, I'm not convinced you burn more calories with
HIIT, I'm more convinced that you burn more fat. The idea behind
HIIT, or at least what the National Strength and Conditioning Association claims it to be, is that it targets certain energy-producing systems in the body. When you do a 1:1 - 1:3 rest-to-activity ratio, you activate the oxidative system of the body - or the fat-burning system.
Energy for workouts comes from calories created by breaking down nutrients in your body. For most exercise, the primary source of these calories is carbohydrates. The source of these calories is determined by the bioenergetic system of your body in use, and THAT depends on the level/duration of the activity in question.
The oxidative (fat burning) system is used primarily for extremely low intensity activity (your day-to-day routine) and once your carbohydrate stores become limited. When you do
HIIT with a 1:1 - 1:3 ratio, your system is shocked, in a manner of speaking, into using the fat-burning energy system BEFORE the carbohydrate energy system. This means you're burning fat right-off-the-bat, whereas otherwise you'd have to exercise for 20 minutes before you really started burning any significant amount of fat.
Of course,
HIIT can also be used to target other systems with different rest-to-activity ratios, but the lower the ratio, the more you're targetting fat burning.
One of the major advantages to
HIIT is that you can burn fat without burning much muscle, so it's ideal for cutting and general weight loss - whereas with long-endurance workouts (which is what you'd normally do for weight loss if not
HIIT) you tend to burn more muscle as your body cannot liberate carbs/fats quickly enough (so it must burn muscle protein for calories).
One downside to
HIIT is that you're not getting as great a heart workout, which of course is something you want.