You have to consider that they have absolutely nothing else to do but eat healthy and exercise. Obviously, this doesn't apply to the average person. On that show, they are exercising a good 5 hours per day. Given the very high weight of the people on the show, they could easily be burning 500 calories per hour (or much more depending on the activity; my top estimate would be 800-1000 calories/hour). So, if you burn an average of 500 calories/hour for 5 hours, that's 2500 calories per day. Now, at their weight, they could probably eat about 2,500-3,000 calories to MAINTAIN their weight. So, assume that their diets on the show are about 1,500-2,000. So, they have a 1,000 calorie deficit in their diet. 1,000 (diet deficit) + 2,500 (exercise) = 3,500 calorie deficit/day. So, that is one pound per day leading to 7 pounds/week. Now, sometimes they exercise even more and eat even less (or weigh more), which could lead to even more weight loss.
This isn't even including the fact that was mentioned before which is that one week on the show may not be one week in real time. If they actually have two weeks, 14 pounds/"one week" show could be possible, etc. Unless you can dedicate several hours per day to exercise like they can, you won't be able to lose weight that quickly. However, it is better to lose weight slower! Your muscles will have more time to develop, and your skin will have more time to adjust to your new size (hopefully decreasing saggy skin/stretch marks).
One thing to note, however, is that exercise is the key for them, and could be for you. If you lose weight by cutting calories and don't add any exercise, your muscles will be eaten by your body (dramatic, but true). You need to at least have a little toning or some form of activity to help push you into burning the fat instead of the muscle (if you absolutely can't exercise, eating a slightly higher protein ratio than the standard 10-15% will also help to maintain muscle mass; suggestions on this forum are about 30%, and that seems reasonable to me since you can still have a good 30% from carbohydrate which the body likes to fuel your brain and nerve function). So, if you are looking to speed up weight loss, adding exercise is way healthier and more efficient than cutting your calories extremely low (remember that strength training builds muscle which increases your metabolism at all times and cardiovascular training can vamp up the metabolism for up to 12 hours after the activity).