The major difference between these three groups is that carnivores eat meat, herbivores eat plants, and omnivores eat a little of both. Each has a different kind of teeth and digestive system that helps it eat and digest its food.
Carnivores have only one stomach and sharp, strong teeth made for tearing into meat to get if off the bone. They spend little time chewing their food, because their saliva lacks digestive enzymes to help them break down the food. The animal sends it directly down to the esophagus where the digestive process begins. The food enters the stomach where it is digested and the nutrients extracted.
Herbivores only eat plant matter. They spend a lot of time chewing their food with flat teeth made for grinding tough plants. The food reaches their stomachs where it is fermented to make for easier digestion. During the fermentation process, a special microflora is excreted which helps to break down tough plant matter, making the nutrient extraction process easier.
Omnivores eat both animals and plants. Humans are a prime example of omnivores. The digestive system of an omnivore is more like that of a carnivore but they can more easily digest plant matter than most herbivores.