I'll explain because if it doesn't make sense I can only conclude that you don't really know how it works or have an over-reliance on your AE Lock button.
When you are taking photos in A mode for instance, you have control over 2 of the 3 elements that make up the exposure. You can control the Aperture, and the ISO. Whatever you set these to the camera will set the shutter speed to keep the exposure constant. That is in A or S mode you have NO control over the exposure as the camera selects it.
Shot at ISO400 at f/2.8 and the second at f/4.5
Yes but I wanted to be able to see what colour my wall was. Notice that changing the setting doesn't affect the image brightness. The same was as changing the ISO won't affect this either. The camera will simply compensate by adjusting the shutterspeed to keep the wall black.
Now this one is shot at f/2.8 with Exposure Compensation set to +2
Like my plain light yellow/grey wall?
Not using exposure compensation you're making the assumption that the camera knows what you want to photograph. Like photographing a person against this window I would like the subject to be lit correctly and a brilliant white light to be streaming through from the back. I can't do that in A or S mode without exposure compensation since the camera will assume the image is overexposed.
This makes no sense in M mode since you have complete control but if I wanted to simply point and shoot and let the camera try to guess how to take the photo I would have bought... well a point and shoot camera.
/EDIT: My sister's $100 P&S has exposure compensation too.