I'm still confused. Are you saying that my lens would autofocus at f5.6 or f6.3 but not at f8 or f11 and that I should be using manual focus at any aperture smaller than f5.6?
No, in this case, its referring to the maximum aperture a lens has. For example, a 100-400 has a max aperture of f/5.6 at 400mm, and so it will auto-focus on all Canon cameras. If you stop it down to f/8 or f/11, it will still autofocus. However, if you put a 1.4x converter on it, you've turned it into a 560mm f/8 lens, and it will no longer autofocus on most Canon bodies (1D series and 5dIII aside). The autofocus system relies on light and contrast to focus, and you've made it too dark a lens for the auto-focus system to work reliably.
Now, technically, it will auto-focus at f/8 or f/11, but, odds are whatever you are shooting has moved on in the 5+ seconds it took to lock focus. And in some cases, it wont lock focus at all.
So, gaining f/8 auto-focus is more about the ability to use teleconverters on lenses that are already a little slow. A 2x on a lens that ends at f/4 or a 1.4x on a lens that ends at f/5.6. Generally its important for wildlife shooters, which is why it makes sense that a 7DII might have it (and say, a T5i wouldn't)