First off, I'm going to push the disclaimer that I do NOT support low carb diets. There is a substantial amount of literature available online that supports low carb diets, and there is an equally substantial amount against low carb diets. I'm a first year med student; I still don't know how to do a chest exam; you should not be consider this post serious, medical dietary advice.
Now that I've got the disclaimer out of the way, let's take a look at the science behind a low carb diet. Low carb diets can be high protein diets (Atkins) or high fat diets or a combination of high fat/high protein. The key is to reduce your carbohydrate intake.
If you have ever seen someone on any variation of the carb diet, you may have heard them tell you that they have seen immediate results, such as losing 5-10 lbs in a week. You should realize that if you ever lose weight this quickly, unless there is an extreme circumstance, you have lost water weight, not fat. Low carb diet results in water shedding because your glycogen stores are burned (see the previous metabolism post) and not replenished. One molecule of glycogen normally carries 3 molecules of water with it; thus, if you have less glycogen in your body, you have less water in your body. This depletion of glycogen is responsible for the immediate weight loss.
The low carb diet can lead to fat loss in the long run. Low carb means low sugar, and low sugar means low insulin. Insuling promotes fat storage and prevents fat cells from releasing fat into the blood. Without sugar, fat is released to the blood and used by most cells to generate energy. Also, protein and fat lead to satiety (feeling full), so having a high fat/high protein diet can cause you in eating fewer calories overall.
Again, I am NOT suggesting that you start a low carb diet. Altering the proportions of your diet to include more fat or protein can lead to alternate health risks in extreme cases. Too much protein in your diet can cause nitrogen related damage. Too much fat in your diet can cause blood fat to increase, which can cause cardiovascular health concerns. So in the end, if you want to lose weight, talk to your family doctor!