So this topic comes up a lot in these forums, and I thought I'd try to lay it to rest with a top-level post. This information comes from Gary Taubes' lecture last summer, which can be seen here:
Check it out from about 45:00 to the zinger that comes in at about 52:50.
In a nutshell: Almost all hormones in the body (except insulin) tell the fat tissue "dump fatty acids into the bloodstream so we have fuel available." They move fat out of the fat tissues. Insulin does just the opposite. It moves fat into the fat tissues. Additionally, the hormones that metabolize fat, including HGH, can't do their jobs if insulin levels are elevated - the insulin always trumps. If you eat carbohydrates, you elevate your insulin levels. If you elevate your insulin levels, none of the fat-metabolizing hormones can do their jobs.
So you have to lower your insulin levels in order to burn body fat. Otherwise, the body holds on to what it has in the fat cells, and your dietary fat gets stored as well. BUT! In order for insulin to store fat in the fat cells, it needs a particular substance called "glycerol-3 phosphate" to break the dietary fat down into fatty acids. Otherwise they can't get into the tissues.
Guess what glycerol-3 phosphate is produced from?
If you guessed "dietary carbs," you got it in one. The body can't produce very much of it at all on its own.
So if you aren't eating any carbs, your body doesn't have the substances necessary to move dietary fat into the cells. Therefore, the dietary fat that doesn't get immediately used by the body gets flushed out as waste. And since your body needs fuel all the time, even when you aren't eating, if there's no dietary fat around to burn, it'll burn adipose tissue - stored body fat - because you aren't eating carbs to stimulate insulin to block the other hormones that metabolize fat, or to produce glycerol-3 phosphate from glucose metabolism.
This is why we can eat very low-carb or no-carb diets, with their huge amounts of fat, and not gain weight and actually lose weight. The carbs DO matter. I know a lot of people here don't want to hear that, but Mark's carbohydrate curve is correct. Get above 100 carbs or so a day and you're asking for trouble. No, it's not Atkins, but the fact remains that the more carbs you eat with your fats and proteins, the more likely it is that those fats will be stored instead of used or flushed out. And you'll gain weight.
I try never to go above 50 carbs per day maximum, and my weight is still coming off at a rate of about two pounds a week, and my blood sugars are still hanging out right around the 90-95 range. Half of an avocado or a single handful of berries is enough carbs and then some. I am determined to deprive my body of glycerol-3 phosphate whenever possible, since that's the real mover and shaker when it comes to fat storage.
Go watch the vid, too.