I think there's a bit too much "pot" going around, if you know what I mean...
I found these links to be much more useful than that diagram. Two of the best tutorials (in my opinion) are:
IceHardware
and
this one
Hopefully one of those will explain it for you.
Whether you need a potentiometer will depend on whether you want to be able to adjust the backlight. You could wire in a switch to change between full power and half power for day/night use, or just use the pot to adjust it to a comfortable level. Either way, check the specs on your LCD. I found my LCD needed 4.4v, while one of the sites said straight 5v is okay. Had I wired it that way, I would have fried the backlight. Check and double-check your specs. I've even had two LCD's from the same manufacturer use different specs.
Good luck,
Kris