f#.# is the largest opening the lens's aperture (opening) is capable of. With f stops the smaller the number the larger the opening. I believe each stop down lets exactly half the light of the previous stop. Lenses that are capable of large apertures - f2.8, f2, f1.8, f1.2 (or the famous Canon 50mm f1.0L) are considered "fast" lenses (in that one is able to shoot at higher shutter speeds because of the larger aperture the lens is capable of). All lens "stop" down to f22 or beyond so the max aperture the lens is capable of is always what's listed. When a zoom is listed as, for example, 28mm-135mm f3.5-5.6 it tells you the max aperture at 28mm is f3.5 and at 135mm f5.6. Some zooms like the popular Canon 70-200 f4 are capable of the same aperature across the zoom range.
The benefits of a "fast" lens are:
Much better auto focus at low light conditions.
Easier to use high shutter speeds which freeze action and give sharper pictures.
Better view finder illumination on an SLR.
Capable of more and nicer "bokeh" or background blur.
The disadvantages are:
Much larger physical dimension. For example the Canon 400mm f2.8L IS is huge (3 times the size) of the 400mm f5.6L.
Due to the size of the lens elements needed, much greater glass quality (and therefore expense) is required to produce alens which has a great image when shot "wide open".
Garrett Cortese has a nice primer on all this on the wakeboarder.com media/technology forum which is worth reading.