Another topic I struggled with a bit as a complete noob, Aperture.
Aperture is the diameter of the actual opening that light will travel through to hit the sensor (or film).
Its defined by an F number (or F stop, or aperture value) ie F2.8, F3.5, etc...
Contrary to what one might immediately think, the smaller the F number, the larger the aperture. ie F2.8 is larger than F3.5
The "chart" below illustrates FULL F-stops and the corresponding shutter value required to get the same exposure at each stop.
F1.8 F2.8 F4 F5.6 F8 F11 F16
1/2,000 1/1,000 1/500 1/250 1/125 1/60 1/30
In reverse you can see that having an F2.8 capable lens would let you take the same shot at twice the shutter speed as an F4.
However, lets throw ISO back into the mix. Say you are framing a shot that allows for 1/60s F4 ISO1600, you could take the same exposure at 1/60s F2.8 ISO800. Using a lower ISO is often desirable to reduce noise and exploit the most from your sensor.
Unfortunately this leads to the next topic as larger apertures don't just let more light in, they can reduce the depth of field within your image.
Depth of Field
Depth of field refers to the amount of depth within your frame that will appear in focus. Deep (or great, or whatever) depth of field will render pretty much everything in focus. Shallow depth of field can render very little of the frame in focus, providing for that nice out of focus blur.
Very loosely, larger apertures will decrease depth of field and smaller apertures will increase it (dependent on focal length to an extent).
If you are after that shallow depth of field blur, using a longer focal length with large aperture will decrease the depth the most.
If you wish to have your entire frame in focus, F8 will usually accomplish that on a crop body D-SLR, a little smaller say F10-F11 on a full frame digital or film.
Why smaller aperture on a full frame?
Well the same framed image on a full frame will be at a higher numerical focal length (ie DX 17mm = FX 25.5mm) which as I mentioned can increase the shallowness of the final result, so you need a slightly smaller aperture to offset.
Bokeh - That out of focus blur
Bokeh is the name given to the blurred focus appearance within shallow DOF images. Some lenses have a nicer bokeh appearance than others, but this is generally a subjective quality.
Note for P&S owners.
It can be very difficult if not impossible to achieve a shallow DOF image on a P&S because the actual focal lengths are extremely small and they generally don't offer particularly large apertures either. Using the Canon S5 as an example, its lens is a 6-72mm (equivalent to 36-432mm) with a max aperture of 3.5 on the long end.