After high intense bouts of exercise, your body tries its darnedest to return your body to a state of balance. Specifically, it works extra hard to get more energy into your muscles and puts more orxygen into your blood (both of which were drained during the HIIT exercise, at a much faster rate than if you were simply sleeping. So, after you have these periods of intense exercise, your body is actually converting energy to your muscles at a higher rate than normal!
Because this is all occuring AFTER you exercise intensely, rather than a nominal walk or slow-paced elliptical effort, intense bouts of exercise have a profound effect on the weight loss experienced for hours after exercise. To the contrary, low-moderate exercise in the so-called mythical "fat burning" stage do not help nearly as much. Therefore, it is rather safe to conclude that the longer the intense exercise, the longer the recovery period, which means the longer the EPOC period remains....therefore, the more fat lost as a result of your exercise.
A lengthier article appears here. This isn't necessarily new to the fitness world. P90, P90X and P90X2 all were based on the principle of HIIT (high-intensity interval training) simply because the effects of EPOC are so significant. But, even if you don't use these training programs, its good to incorporate bouts of intensity into your current exercise regime. If you walk on a regular basis, run 100 yards every mile! If you jog on a regular basis, sprint for 100 yards every mile. And if you simple love the elliptical, every 10 minutes or so, jump up the RPMs to something stellar and try your best to keep them high for a few minutes! Draining your muscles and oxygen as a result of these bursts of intensity have effects on your fat burning ability for hours afterwards. In fact, you can lose more weight doing this less hours/week than your current effort. Now, coupled with the fact that incorporating these bursts of intensity have other benefits (eg if you are a runner, doing these "fartleks" will likely increase your speed and stamina, for instance), so what the downfall for trying?