HIIT is the acronym for High Intensity Interval Training. It means that you exercise in bursts of activity with small breaks of rest in between or lower intensity exercise. For example, you run fast as you can for four minutes, then you walk for 2 minutes. Or you do an exercise for 2 minute as many times as you can with correct form, then you rest for 1 minute. So you burn more calories and you build muscle in less training time than with running at a steady pace or with conventional exercise. HIIT programms usually last from 15 minutes to half an hour, 3 times per week at most. They are good for people who have a busy life or don't want to spend a whole morning in the gym. HIIT programms are demanding, so the rest of the week days one can do lighter exercise, such as yoga or jogging.
HIIT increases the demand of the body for oxygen. When the oxygen it gets from breathing isn't enough, it breaks up the fat to get the energy it needs. And you get a faster metabolism, and you keep burning fat even after you exercise. It doesn't increase appetite, since it reduces grehlin, the hormone that induces hunger, and it increases the amounts of lactase and glucose in the blood, that help control hunger.
The single most well-established benefit of interval training has to do with heart health. Intervals can boost cardio-respiratory health with a smaller time investment compared to continuous forms of exercise.