The larger the mm the closer the subject appears. Action usually means sports or similar which you can't always get close to so you need a higher "Zoom" to get the image you are after.
"L" glass is basically Canon's version of higher quality glass used in the lens which gets better photos. Usually used by professionals. This is Canons explanation:
"these lenses use special optical technologies [such as] Ultra-low Dispersion UD glass, Super Low Dispersion glass, Fluorite elements, and Aspherical elements to truly push the optical envelope."
Simply, the lower the f# the less light that is needed while maintaining the same ISO. Say you are shooting a Baseball game at noon, the 5.6 will do just fine. Say you are shooting a game at dusk, the 5.6 will be very dark while the 2.8 will still come out decent.
I know it's a lot more technical than this but it gives you an idea of what it all means and why.
Hope this helps a little.
Oh, and please don't get caught up in the "Higher megapixel = Better Prints" debate. There are other factors involved that make this not exactly true.