You will consume less simple carbs. This means two things - first, you will limit the amount of sugars that your body has to burn immediately, and second because you are limiting your simple carbs you are not consuming all the fat that goes along with this food group (not fruits and some vegetables).
Remember, you are on a diet so you are trying to reduce the amount of fat you consume.
With a reasonable level of physical activity you will burn the small amount of sugar that you are consuming and then you will begin to burn fat. This is what we want!
You can consume some of the carbs you like but not at the same level as Atkins.