Not every camera has the possibility to select manual aperture settings. Most will select a fixed combination of shutter speed and aperture at a given Exposure Value. This will do fine for general photography, however there are times when you may want to adjust aperture manually.
When taking < landscape photographs> for instance, the object mostly is to get everything from foreground to background in sharp focus. So you will need large depth of field. To achieve this, set an aperture of 16 or 22. In aperture priority the camera will then automatically select the right shutter speed but in full manual, you will have to decide the right shutter speed for a correct exposure of the scene.
If you would like to isolate your subject from the background, for instance when taking portraits, open up your aperture to throw the background out of focus. Apertures of 2.8 or 4 will focus attention on your subject while keeping the background blurred.
The effect is even stronger when using tele lenses as their depth of field is very shallow at any setting. With wide-angles the effect of a large aperture will be less obvious.
When taking macro photos, manually select a small aperture (16 or 22) to get as much depth of field as possible.