Can someone explain to me in layman's terms the difference between the Asus UL80AG and Asus UL80VT?

The difference here is actually quite mive. The UL80AG has an embedded graphics card, which means that it doesn't actually have an entire card dedicated to graphics. Instead, it just has a couple chips on the motherboard for graphics. If you plan to play any kind of games or do anything that entails a lot of media processing, you need a dedicated card or you will have a lot of lag. The dedicated card in the UL80VT is a lot better and will give you a smoother experience overall.