Six while the calories in/calories out concept isn't quite as simple as it's made out to be, it still holds. Part of the issue is that some foods take more effort to digest than others, like the myth about celery being negative calories. It takes more effort for your body to digest protein than it does carbs. Also if you're consuming less than 150g carbs per day then your body converts protein to carbohydrate by gluconeogenesis which is an inefficient process, off the top of my head it's something like 60-70% effective so to produce 10g of glucose you need to use up 15g of protein. A low carb diet still produces a calorie deficit and that's why you lose weight. Basically by reducing insulting production you allow fat to flow freely in and out of your fat cells as triglycerides. (When insulin levels are high fat can only flow into your fat cells). When you're fat-adapted your body uses up all these lovely triglycerides floating around: your muscles use the free fatty acids directly, your liver can convert the glycerol backbones to glucose to feed your brain, retinas and red blood cells, and your liver also converts the fatty acids into ketones which your brain also uses. Because you have this ample supply of fuel in your bloodstream your food consumption drops so your calories in is less than your calories expended, with the difference coming from your fat reserves... hence you lose weight.
As you get towards your target weight the process of weight loss usually slows or stops. This is where tracking calories can come in helpful. In my case I was still eating the portions I needed when I was over 11 stone so My Fitness Pal allowed me to see where I was going wrong. I almost feel like I don't eat enough now because my portions are so much smaller; now I know the feeling of pushing away half a plateful of food because I'm stuffed. Whereas before I would have just eaten everything I was given because that's the way I was brought up. Another issue when near goal is that sometimes you need to increase the amount of fat you are eating as your fat stores are much smaller and strangely increasing your fat macro can lead to a sudden drop on the scales.
If you are a stone or more overweight then follow the Bootcamp rules and you should lose weight easily enough. It's only when you get within half a stone of goal that more tweaking may be required.
There have been a few people on these threads that have experienced an extended stall in weight loss despite being somewhat over their target weight. In that case there are tweaks such as cutting dairy, avoiding artificial sweeteners, reducing nut intake etc. that can help. I also have a theory that sometimes your body resists losing weight as part of a homeostatic balance mechanism where it is adjusting your weight set point to a new, lower, point. That would explain people like myself and Miffy who cannot get the scales to budge downwards but hover around the same weight for an extended period.