Attack Speed is exactly what it says, it increases your attack speed by speeding up the animations your character does when it performs one of it's skills, this is why it's useful to casters as well as melee classes.
Without any items that give Attack Speed your character usually has 1.00 attack speed. You can think of it as x1 speed.
If you wear an item that gives 10% Attack Speed, it will increase to 1.10.
Adding a total of 100% Attack Speed will make it 2.00 (x2) meaning your attacks speed will be doubled. You can't go any higher than this, it's capped at 2.00 (or will be when I update, it's currently 1.90/1.99 as I mentioned in my earlier post).