First off, as some have discussed above, the out of focus area is commonly refered to as bokeh. And if you want the subject to be sharp, and the rest of the area thrown into an array of defocused splashes, then I would think a more agreeable term to use would be "a shallow depth of field". Everything from the foreground to the background being pin sharp is refered to as .. errmm..... I'm not sure myself, but along the lines of deep, broad depth of field.
The amount a bokeh (or blurness in layman terms) depends on to components, mainly the focal length and aperture. I will briefly explain here, as this is a common topic. The larger the aperture (f2.8 is larger than f4, f8 is larger than f22), the blurer the background. The longer the focal length (layman terms commonly refered as zoom), the blurer the background. In my opinion, focal length seems to have am overal larger effect on the blurness.
Now, how do you get a very blur background with a digital compact ? The sad thing is..... its difficult. Digital compacts have exceptionally short focal lengths compared to SLRs, and so it is nearly impossible to get any bokeh at all, even when u have large apertures. The Sony f717 was able to do it because it has a huge zoom, but even then, the focal length is still pretty short. But anyway, the best u can do is to shoot at the longest focal length on your cam, with the smallest aperture. Set the subject nearer, with the background further.
I jumped to a D100 dslr from an A40, purely for bokeh.
This was done @ 70mm f2.8 . On a digital compact, and equivilant to a 70mm would probably be around 300-400mm zoom.... which would put the subject too far away... so there is hardly a substitute for the real thing.
Its a pity really. If u must, use photoshop to achieve this. But even then, it will take u days of editing to perfect the real thing.