Okay...here's a couple of pics for comparison.
Exif info: shutter 1/800 aperture f4 focal length 300mm iso 200
Exif info: shutter 1/30 aperture f32 focal length 300mm iso 400
Both shots were done using aperture priority (you set the aperture/f-stop and the camera basically does the rest for you) on auto. F4 was the lowest that the lens was capable of and went as high as f32.
You can see what the difference in aperture does to the background (btw, sorry about the blurriness of the 2nd pic; still trying to get used to a 3lb 100-300mm f/4 lens...more on this later). When the aperture is higher (2nd pic), both the subject matter and the background is in focus and vice versa (background blurred while subject matter remains in focus at lower aperture).
Also, check out the shutter speed. It's much slower when there's less light entering the lens (at f32, it's 1/30 of a sec.). Just by altering the aperture, it was much easier to take the picture and the difference in shutter speed is very noticeable (you can even hear the difference). Even when the lens is a bit on the heavy side, it can still be handheld (in other words, setting a lower aperture will also help if your hands are shakey).