f/2.8 got larger max aperture, which means you can shoot with higher shutter speed in lower light, and depth of field is narrower, creating a nicer effect if you want isolate your subject from the background.
It also means more glass, and that mean the price would be higher.
if you don't know the difference, then you probably shouldn't bother about the difference.
that said, read and learn about how various parameters which you can adjust in photography can affect your photography. they may not improve your composition, but you can definitely achieve a lot more variation and certain effects that you desire if you understand such technicalities.
for aperture, there would be 2 issues when it comes to buying a lens with a larger maximum aperture - as others have mentioned, depth of field (isolation of subject from background) and the fact that you can shoot with faster shutter speed in low light. i.e. given the same scene, a f/2.8 lens might be able to avoid handshake better than f/4.0.
every setting usually has two linkages to your photo - be it iso, shutter speed or aperture. one would be exposure, the other would be the result that you see in the photograph taken.