What is the difference between simple battery and aggravated battery?

Keep in mind that this is dependent on the jurisdiction in which we're referring to, but in general:

Battery is touching someone in an offensive manner. The most common examples are punching, hitting, or kicking someone, but it can also be used for sexually motivated crimes. Hence, the crime "Sexual Battery".

Aggravated Battery, in general, is "Battery with a Deadly Weapon". This may involve stabbing, shooting, or even hitting someone with your car.

Some areas also use aggravated battery for "battery that causes extreme damage". So, it's possible that if you hit someone, and break their jaw or knock out several teeth, you could be charged with aggravated battery.

But, as I stated up top, this is dependent on your local laws.