always thought that the F-Ratio in SLRs/DSLRs, which I sometimes refer to as F-value or Aperture Opening Value, has something to do with the amount of light it would allow to enter the sensor or film. Like tuning the ISO setting of a camera, it would be like changing the value of brightness or gamma correction in the resulting picture.
From this free book supplied by Canon, I later got to know that the F-Ratio mainly deals with the focal length...and the brightness variations are only 'side-effects' from the change of opening size. As it turns out, the larger the F-Value, the smaller the apperture opening becomes, therefore the farther the focal point gets. The difference which you can see below as the F-value gets smaller, the nearer the focal point gets, which in turn focuses on the subject and blurs the background.
The photo first photo on the left uses an f-Ratio of 13. Notice that all the features of the background is in focus along with the subject. The next photo on the right uses an f-Ratio of 3.5, making the background blur out while maintaining focus on the subject. In both cases, I had to adjust my shutter speed to compensate for the difference in brightness. I theorized that this is all the difference you get from a standard 18-55mm lens, I think I need to get my hands on some 28mm and 100mm's to really see the difference.
Playing with this feature can get you those shots that makes it look like you're using tilt shift lens but on a more smaller scale.