As I have explained elsewhere, macronutrients are the "big" basic calorie sources in food. There are only three: protein, carbohydrate and fat. Each of these macronutrients have very different properties. Protein is essential in large amounts (~50-60 grams daily MINIMUM), some "essential" fats are required daily but in far smaller amounts and finally, carbohydrate is the only macronutrient that is not absolutely required for human life.
At any rate, one very popular approach to weight loss over the years has been to restrict either carbohydrate or fat intake (restricting protein is deadly). Thus the two basic types of so-called "macronutrient restricted diets are "low fat diets" and "low carbohydrate diets".
If you look at the diagram to the left you can begin to understand the relationship between these diets. Generally low-fat diets are very high in carbohydrate, extremely low in fat and "lower" in protein (because meats are a big fat source). The reverse is true for low carbohydrate diets. I have draw the relationship out as a continuum in order to show something else as well. Namely, most popular diets fall in between the right and the left but do, to lesser and greater degrees, manipulate macronutrients as well. But classical macronutrient-restricted diets come in only two flavors: low-fat and low-carbohydrate.