Hope you had a look at the artical on basics of camera.
Unit of the size of an apaperture is f-stop. An f-stop indicates the size of the aperture with respect to the [effective] focal length of the lens [attached to the aperture]. Physical size of the aperture (i.e. the diameter) is reciprocal to the f-stop of the aperture. Meaning the bigger the f-stop, the smaller the physical size of aperture. See figure below.
Note: Why use some creepy thing like f-stop when you can represent the same thing using a simple unit like milimeters [for diameter]? Well, using f-stop makes the unit independent of the focal length of the lens, so when you say that there are 2 lenses [having different focal length] with aperture = f/2 you know that both of them allow same amount of light to pass through. But if you say that there are 2 lenses [having different focal length] with aperture = 12 mm, both will NOT allow same amount of light to pass through.
Refer to: Wikipedia: F-stop for details.
Now lets look at the side-effects of different aperture size. This is where the optics comes in.
If the aperture is big we will have deeper depth-of-field or DOF. What is DOF you'll ask? Technical definition of DOF is the distance (perpendicular to the camera) in which the subjects have a clear focus.
Photo below gives you an idea. As you can guess the left most was taken using big aperture (say f/1.4), where as the right most was taken using a smaller aperture (say f/22). Refer to Wikipedia: DOF. Difference can be seen clearly when you see how well the columns far from camera are in/out-of focus.
1. When you are taking portraits: (Portrait photography is a style of photography). Photo below (courtesy photo.net) is a bright example of a portrait. This photo is taken with a big aperture. Imagine if the you were to see all other details (e.g. the building in the back- ground and the street light) would the photo have same impact? So usually a portrait photographer uses a lens that supports a big aperture (f/2, f/1.4, f/1.2..)
2. When the ambient light is low e.g. in late evening. As we learned earlier if the brightness of light is less AND the camera's shutter speed can not be slowed down below a limit (so that the light is allowed to expose the film for a longer time) then one is forced to use a big aperture so as to keep shutter speed at an acceptable value. Refer to shutter related section for some more info.
Now we know when to use a big aperture. So it's implicit when to use a small aperture ! When taking pics of landscapes (gardens, mountains, rivers city block/street) or architecture (castles, buildings, towers) one would want to capture details and not only a part of what is seen so these are the situations where you close down your lens to say f/8 or less (less means f/11, f/16..).
See the landscape photo below for example. Everything near, far and in between adds to the picture, we wouldn't want any of the boats or the clouds (which are far away) out of focus.
A bit more of jargon about lenses. Camera lenses' specification would provide the biggest aperture size that the lens can handle e.g. "Canon EF 50mm, f/1.4". It means the lens' focal length is 50mm and largest aperture it can handle is f/1.4. The lower limit (smallest aperture supported) is usually not of interest as most lenses support small enough aperture to take care of most photographic needs. When a photo is taken at the biggest supported aperture of a lens it's called "lens was kept wide open", the opposite of that would be "lens was closed down".Finally, lenses with bigger max aperture cost more than those with smaller max-aperture, e.g. Canon EF 50 f/1.2 costs $1500 whereas Canon EF 50 f/1.8 ii costs $110!!
For zoom lenses f-stop spec is usually provided at both ends of zoom range, e.g. Canon EF 28-105 f/3.5-4.5, means when lens is set to 28mm, max aperture is f/3.5 and when lens is zoomed to 105mm the max aperture is f/4.5, min aperture in both cases would be quite small like f/16-18. Lens with a fixed focal length (e.g. the 50mm above) is known as a prime lens.
To summerize:
- Bigger the aperture (smaller the f-number) shallower the DOF. Useful in low light conditions as well as portrait photography.
- Smaller the aperture (bigger the f-number) deeper the DOF. Useful in landscape, architecture and other forms of photography where details of most things in frame are expected to be clear/in-focus.