The Glycemic index or GI is the secret behind the south beach diet. It is not a low carb diet but a low GI diet. Quoting from Wikipedia:
GI is a measure of the effects of carbohydrates on blood sugar levels. Carbohydrates that break down quickly during digestion and release sugar rapidly into the bloodstream have a high GI; carbohydrates that break down more slowly, releasing sugar more gradually into the bloodstream, have a low GI.
When sugar enters the bloodstream, the pancreas secretes insulin which triggers cells to absorb it. Many years of introducing quick bursts of sugar would eventually result in cells becoming resistant to insulin. This resistance would leave sugar in the bloodstream longer which would then cause the pancreas to release even more insulin. This excess insulin would eventually drive blood sugar below normal levels. This in addition to potentially causing diabetes, is what makes people hungry!
excess sugar consumption ------> excess insulin -------> low blood sugar --------> hunger pangs ----------> consumption of more sugar.
This is why we feel hungry very quickly when we eat a donut and not when we eat an egg for breakfast.
Cutting down the sugar intake by reducing direct sugars eaten as well as by blocking the bad carb pathways you can reduce the hunger pangs, thus consuming lesser calories. You don't crave foods so you eat less and this leads to weight loss.
Another way the diet helps is by causing Ketosis. If there is not enough glucose (from carbohydrates) in the bloodstream the body draws on fat stores for fuel, causing the appearance of ketones in the blood. Ketones are produced by the liver from fatty acids. They are small carbon fragments that are the fuel created by the breakdown of fat stores.
When the body is in ketosis the individual tends to feel less hungry, and will probably eat less than he/she might otherwise do. The body switches from being a carbohydrate-burning organism into a fat-burning one. The fat stores become a primary energy source, and the person loses weight. This must be done in moderation (max 2 weeks) since it is not a sustainable healthy thing to do.
So to sustain & keep healthy, it is good to eat a healthy mix of protein, vegetables and "good" whole grain carbs that the body takes longer to digest. Think about it, and you may do your body a favor!