A soft, blurred background isolates the subject in a photograph. Consumer level point-and-shoot cameras typically try to keep the entire scene in focus, which can be distracting when there are many background elements. The blurred area in the background is called the "bokeh," and appears when the photographer uses a narrow depth of field.
Calculate the appropriate depth of field for your subject. A very narrow depth of field will keep only a few parts of your subject in focus (such as a person's eye or a flower's petal), while a wider depth of field will keep the entire subject and even some of the background in focus. A depth of field calculator will help you to determine the appropriate focal length, distance to subject, and aperture to use.
Select a large aperture (low f-stop number) to narrow your depth of field. An aperture of f/2.8, for example, will create a very narrow depth of field, while an aperture of f/8 will create a much wider one.
Increase your focal length. A longer focal length will narrow your depth of field and increase the amount of bokeh.
Move closer to your subject. Assuming your aperture and focal length are kept consistent, photos taken closer to your subject will have a smaller depth of field than photos taken farther away from your subject.