Carbohydrates such as sugars and starches are turned into fat by your body because of insulin.
The idea behind a no or low carb diet is that if you remove most or all the carbohydrates sources from your diet, then your body will begin to burn the stored fat, making you lose weight.
The different diets out there that decrease your daily carb intake work because they limit the amount of insulin your body produces, which makes your body use any fats that you eat as fuel, instead of storing them as fat tissue. Without your body forcing insulin secretion to store the fat you will lose weight faster and easier.
One thing to watch out for is how a low to no carbohydrate diet can change your metabolism. As a normal response, your body automatically shuts down when it no longer has energy normally received from carbohydrates and acts by slowing down your metabolism, making it difficult to lose weight.
While you do lose a lot of weight while following this drastic diet, be careful in limiting too much carbs from your diet, as it can affect your health.
Usually the diets out there let you have a very small amount of carbs, most coming from whole grains, and with this moderation you can lose weight safely and healthily.