[dcclark]

f/stops have become a sort of fundamental measure of how you can change an exposure. First, numbers: f/stops come in multiples of the square root of 2 (which is because they're related to the size of a circle... mathematical details available if you really want!)

So starting at f/1, FULL stops go:

f/1
f/1.4
f/2
f/2.8
f/4
f/5.6
f/8
f/11 (approx., it's actually 11.3, but basically all cameras use f/11)
f/16
and so on. Each of these is (square root of 2) times the previous one, where (square root of 2) is about 1.4142.

When referring to exposure in general, the truly correct term is "exposure value," (abbreviated EV) which is basically exactly the same idea. If you go from f/2 to f/2.8, your exposure has changed by one f/stop, which is exactly one EV (you have one EV less light coming in). However, technically "f/stop" referrs only to aperture. So, if you go from a shutter speed of 1/100 second to a shutter speed of 1/200 second, you've changed by one EV (but the change in how much light gets in is exactly the same as if you'd changed by one f/stop, as in the above example).

Many cameras measure EV compensation and shutter speeds in 1/3 or 1/2 of an EV (equivalently 1/3 or 1/2 of an f/stop). For example, my Nikon D40 goes from f/2.8 to f/3.5, which is 1/2 of an f/stop (1/2 of an EV). When it comes to exposure compensation, it goes in 1/3 of an EV. Typically, you will see a bar in your viewfinder which looks something like this:

|..|..0..|..|

The dots (.) are 1/3 of an EV, and the lines (|) are 1 full stop.

Hope this is clear and helps!