HIIT, or High Intensity Interval Training is where you alternate between a high intensity period of exercise, followed by low intensity or rest period. For example, if you're performing pushups, then you would want to perform a pushup for 30 seconds, followed by 15 seconds rest.
Interval training is all about how many calories you burn AFTER the actual workout. This is why it is such a great tool for fat loss. Fat loss is not just about how many calories you burn during the workout.
Instead, it's all about how many calories your burn at the end of the day, week, or month. Your metabolic rate is a measure of how fast you burn calories. Here, the higher the metabolic rate, the more calories and fat you will burn.
Steady state, long duration cardio such as jogging or cycling does nothing for your metabolism. This is why you need perform hours of cardio per week, while you only need to perform a few minutes of interval training per day to burn off a lot of fat.
Most people do sprint intervals, but I like to perform interval workouts with bodyweight and dumbbell exercises. This allows me to not only burn a lot of fat, but also to maintain or even build lean muscle mass.
In order to create a good interval workout, all you need to do is choose 2-4 exercises and assign intervals to them. So, with the abovepushup workout, I would add in one more bodyweight movement and two dumbbell movements for a full workout.