If you're asking about merely using a smaller aperture, you'd do that when you want to increase the depth of field, or when you want to compensate for a slower shutter speed.
If you're talking about manually stopping the lens down using the the depth of field preview button, you'd do that when you want to (can you guess?) check the depth of field for the aperture that you've chosen. Normally, the camera keeps the lens's iris wide open so that you have full light available for composing the shot. When you press the shutter release button, the camera automatically closes the iris to the selected aperture and then fires the shutter. Pressing the DoF preview button makes the camera close the iris down to the selected aperture so that you can see exactly what the image sensor will see. The main things that you'll notice are that the view will get darker (because there's less light) and the depth of field will change so that more of the scene is in focus (smaller aperture -> greater depth of field). This lets you check that the parts of your subject that you care about will be in proper focus.