F stop is calculated, based in certain physical lens measurements. I'm not sure of details, but if a lens has a lot of crap glass (cheap zooms) in it, it may actually let less light through, than a good lens (good primes) with the same F stop. Also, it's a ratio, so if you've got a tiny CCD, you need less lens diameter than with a DSLR sized CCD to achieve the same ratio, but as bwana said, DSLRs have bigger CCD pixels, so they can catch more light per pixel, with less noise.
I know, I'm making no sense. Let me put it this way, 35mm needs (roughly) a 200mm lens to make a 4x magnification, but a P&S might get away with a 10mm lens at the same magnification.
And to conclude making no sense, picture quality has got to do with the sensor size, the sensor pixel density, the quality of the lens, the sensitivity of the sensor, etc. And that's just the 'hard' factors, then there are things like focus accuracy and so on that make a DSLR superior to a P&S, even if the specs seem similar.
Edit: Wikipedia makes more sense. F stop is:
the diameter of the entrance pupil in terms of the focal length of the lens
. So if you convert everything to total lumens landing on the CCD, you'll see that your P&S CCD has fewer lumens to work with than your DSLR (for the same f stop), and hence, has a poorer image quality.