As I briefly mentioned in my article on the Exposure triangle Aperture can be explained as the width of the lens opening which lets light into the camera, the wider this opening the more quickly light is allowed in to the camera and onto its sensor (or film).
If you want to allow light in more quickly then you simply use a larger aperture. Aperture is measured in f/numbers generally ranging from f/1 -f/22.
The only confusion comes because the larger the aperture the lower the number, so f/4 is larger than f/16 for example.
Light is measured in stops and common apertures are as follows:
f/1 , f/1.2, f/1.8, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22
Increasing your aperture (eg f/4 to f/5.6) will result in the halving of the amount of light entering your camera and decreasing your aperture (eg f/8 to f/5.6) will result in the doubling of light being let in to your camera.
So which apertures are good in which situations?
Larger apertures like f/1-f/4 result in narrower depth of field (the depth of a scene in focus) which can be useful for throwing the background out of focus for portrait shots where you want your subject in sharp focus and the background blurred so it does not distract from your model.
Middle apertures like f/8 and f/11 often offer the best lens performance so if you do not care about depth of field because everything is at the same distance or you just want the best performance you lens can offer then these middle apertures are a great choice.
Small apertures such as f/16 and f/22 offer the largest depth of field and therfore are popular with landscape photographers who want everything in a scene to appear sharp.
However a word of caution, although these apertures will often give the largest depth of field the issue of diffraction can actually undermine image quality so you may actually be better off using a larger aperture like f/11. A quick explanation of diffraction can be found over on Luminous landscape