Almost every digital camera today, except for your very basic point and shoot cameras, comes with some semi-automatic camera settings. One of these is called aperture priority, usually shown on the camera with some sort of "a" based symbol. Aperture priority mode compliments most camera's shutter priority mode. The great thing about aperture priority mode is that it allows the photographer to have a more control over a shot without going all the way to the camera's manual mode.
In order to use the aperture priority mode, you need to understand what aperture is. The aperture is the size of the opening in the lens when the picture is taken. Obviously, a smaller opening allows in less light than a larger one, so smaller apertures take longer shutter speeds. Aperture is measured in f-stops. These numbers correspond to the size of the aperture or opening when the picture is taken. The most common f-stops are f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16 and f/22. Your camera may have more or less than these.
In aperture priority mode, the photographer sets the aperture and the camera automatically sets the shutter speed for the correct exposure according to the camera's light meter. Different combinations of aperture and shutter speed actually produce the same exposure. For example, an aperture of f/8 at 1/30 will produce the same exposure as f/5.6 at 1/60. However, they will not produce the same picture!
The smaller the aperture the greater the depth of field, meaning that more of the scene will be in focus. The larger the number on your camera, the smaller the aperture (remember these numbers represent the denominators of fractions, so bigger numbers equal smaller settings.) So, f/22 is a very small aperture while f/1.4 is a very big aperture. Watch out, because this can be confusing until you master it.
One more step, and you can see that f/22 (small) will provide a picture where almost everything is in focus, while f/1.4 (large) will produce a picture where only the subject (maybe only part of the subject) is in focus.
One more time, just for clarity:
The bigger the number you select in aperture priority mode, the more of the scene will be in focus.
Digital Photography Composition
What is the point of all this? When you are composing a picture, you can decide how much of the scene you want to be in focus. Your spouse in front of a famous statue needs more depth of field (so that your spouse and the statue are in focus). While your spouse standing on the sidewalk in an unremarkable location needs as little depth of field as possible (so the tricycle in the yard two houses down is not in focus).
Set the camera to aperture priority and dial in a higher number (11) for that statue shot, and dial in a low number (4) for that sidewalk shot. Keep in mind that your camera and your lens determine how low or high you can go in any situation. If you are using a zoom lens, try walking to different distances and using different amounts of zoom to get other options. A lens that only allows for f/8 and higher at full zoom might allow f/5.6 or even f/4 at less zoom. Generally, your camera will tell you somehow (the Canon blinks the shutter speed in the viewfinder) if you have set your aperture set too low or too high for a proper speed to be selected. Dial the number back until your camera likes it. (You can always get more blur later in Photoshop.)
Now you have the ability to quickly control part of your composition without resorting to the time needed to setup a full manual shot.
Check out the opposite mode with Using Digital Camera Settings – Shutter Priority