The main difference between simple and complex carbohydrates is how they are digested by the body. Simple carbohydrates will usually be digested faster by the body, which means that if your body needs energy, it will get the energy from the carbohydrates soon.
Complex carbohydrates will require a bit of time before they can become fully digested. Complex carbohydrates will usually have a long chain of sugar molecules, which means that they will take some time before they fully breakdown.
The good thing about complex carbohydrates is they would usually supply the body with energy for a longer period of time as compared to simple carbohydrates.