See how in the picture above I'm all super sharp in the foreground, and the background is very blurry in a pretty way? That blur is know as bokeh, and is a pain in the neck to get on a point and shoot (which is what I use)
Now, you may find yourself asking "Jen, how do I achieve this illusive effect?" The answer is simpler that you expect! Basically, you use focus and perspective to your advantage. When creating bokeh, basically you making it hard for the camera to keep the whole scene in focus, so It makes the best prominent bit sharp and clear, and the least prominent bit fuzzy. And now what you've all been waiting for, a step by step guide to doing this on your own camera!
Step one: Zoom you camera in the whole way (but stopping once you reach digital zoom. You only want to use optical zoom for this effect)
Step 2: Frame your background. Because your zoomed in all the way, you'll probably need to have your camera super far away from whatever it is that you want in the background.
Step 3: Frame your person (I'm assuming your shooting a portrait) I think I was about 5 or 6 meters away from the camera.
All that's left is for your to press the trigger and take your shot!
Sorry for nerding out about this. It's just really exciting to be able to use such a "professional looking" technique on a very unprofessional camera.