Well, the short of it is that a low carb diet will certainly cause you to lose weight. Yep, it works. And the biochemistry behind it makes sense. Less carbs=less glucose in the blood. Less glucose in the blood=less insulin in the blood. And since insulin stimulates you to store fat, well, you can see how less of it would be a good thing for losing weight. Also less insulin=more glucagon, which is basically the counter to insulin. Whereas insulin stimulates cells to take up glucose and convert it to fatty acids to store up for later use, glucagon stimulates cells to burn those fatty acids. So your body turns over to burning more of its stores in order to keep blood sugar levels high enough to function. The liver breaks down glycogen to glucose so you can function (BTW the brain can only use glucose, it doesn't have any fat it can break down).
But does that mean it is really a good idea? I don't think so. What I am going to lay out here is mostly my opinion regarding the subject, based on my knowledge, so take it in that light.
Glucose is your bodies only form of energy. Seriously. Sure, fatty acids and proteins are important, but nothing like glucose. Glucose is really the starting point of metabolism, the first step in generating ATP. Fats and proteins can be converted and metabolized to enter the Kreb's cycle at other points and can carry out ATP production that way. But that is neither very efficient (results in a lower net yield of ATP for each cycle) nor entirely a good idea. Too much breaking down of fat in the presence of low glucose entering cells and you start to build up keto acids. They are the by product of fat metabolism into the whole metabolic pathway, and just ask any diabetic how afraid they are of ever becoming keto-acidotic. It can become life-threatening, and fast too. Of course it is going to take more for a normal, non-diabetic person to get to that stage, but a lot of that will be determined by their metabolic reserve. Also worth discussing briefly is the fact that for very few people really low carb diets are lifestyle diets. It is just a very difficult type of diet to maintain for the rest of your life, and relapses will pack the pounds on a lot more quickly than they came off. It just isn't very feasible for long term purposes. Sure, there are some who do it, but they are really the exceptions, not the rules.
It all boils down to one simple principle. The only way to lose weight is to expend more calories than you consume. There just is not any other way. Everything is just an attempt to make that easier. And far too often the baggage that comes along with these diets isn't worth it. Now, reducing the amount of simple carbs in a diet is always a good idea. Go for whole grains and fresh fruits and veggies. Having a balance diet that contained less simple carbs (pure white sugar and other highly refined carbs such as white bread-terrible stuff really) in favor of whole grains and complex carbs along with protein and low saturated fats will be much more beneficial, long term, and healthy than just cutting the carbs in favor of more protein and fat.
It is late, that was written fast, so if I didn't make something clear please don't hesitate to let me know!