Tim Ferriss wrote about this specific type of diet, making it an instant hit.
The idea is rather simple: Your body utilizes carbohydrates (sugars) as primary energy source. It needs those carbohydrates to keep your brain running. If there aren't any around in the food, it'll start consuming stored glycogen from the liver and the muscles. Those last about a day, and what then?
Well, turns out that building up fat reserves actually had use! When the stores of easy sugars are depleted, your body will (with some intermediary steps, IANAD*) start burning fat as its primary source of energy.
And that's the secret of the diet that's sweeping the nation right now. By not consuming any carbohydrates, you force your body to start ketogenesis and start burning fats.
Personally, I think there's a second reason why this works: Most meals consist of three components: Some vegetables and healthy stuff for minerals and vitamins and a source of protein (meat, fish, nuts, tofu, mushrooms, etc) for proteins.
Lastly, there's something I call filler: Rice, pasta, potatoes and bread and such, which is basically just lots of energy (calories) to make sure you actually eat enough of those for the day.
By removing that concentrated source of energy in the form of carbohydrates, you've just made it harder to consume energy, meaning that you should lose some weight.
And of course: you get to eat what you want as long as its not containing carbohydrates. Goodbye crisps, fries, bread. Hello steak!
For those interested, some information can be found here
* I Am Not A Dietician