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The difference is in their chemical structure. Simple carbohydrates have a simpler molecular form, and as such are super easy to digest and fairly quick form of energy. Sucrose and Fructose are examples of such simple carbohydrates
 
Complex Carbohydrates, form a larger chain, and come packed with fiber. They have more advanced components that offer better health benefits (fiber) and are digested for more energy. Additionally Complex carbs are used by organisms to store large amounts of backup energy. Examples of such things include Starch (plants) and Glycogen (animals and Humans).

Simple carbohydrates provide energy but for only a short time.

EXAMPLES: foods: fructose – sugar in fruits; lactose – sugar in milk; Sucrose – table sugar.

Complex carbohydrates provide energy for a longer amount of time.

EXAMPLE FOODS: Wheat pastas, brown rice, whole grain breads, cereals.

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