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.