Typically it is used to isolate a subject from a background. This should make the subject the visual focus of an image. Portraiture is an obvious example of this, but the technique is also widely used in all types of photography.
The basic technique requires some understanding of the concept of Depth Of Field.
To get a feel for depth of field start at DOF Master.
In broad terms the technique to get a stronger out of focus blur is :
(a) Use a large aperture ( = small f number )
(b) The subject should be much closer to you than the background
(c) use a camera with as large a sensor as possible
The problem with (a) is that it reduces the depth of field to quite small values. People often fail to understand just how small this can get. Many claims by inexperienced users that their equipment must have a focusing fault are actually due to a combination of failure to choose focus point accurately and a very small DOF.
People may tell you you cannot get a reasonable out-of-focus background with a small sensor camera. This is not true. You can if you apply (a) and (b), however it is more difficult than with a larger sensor camera and the blur is not as strong.
Here is an example taken with an Canon A710 IS :
Lens are often bought specifically for the quality of the out-of-focus blur they create. The relative term is "Bokeh". People speak of "good bokeh" and "bad bokeh". Good bokeh is smooth and symmetric without a structure. Bad bokeh is complex, asymmetric or structured.
Post processing can enhance an out of focus blur, but it is quite difficult to fake a convincing one. This is because the amount of blur relates to the distance the part of photo was from the camera, information which is difficult to estimate from a 2-D photo and which is different at each point !
