I've been searching how to take a photo where the background is blurry and the object is focused. I think I've discovered that my little piece of you-know-what Sony Cyber-shot digital camera will not achieve the photo I want. I read something about changing the aperture priority and I think my point and shoot camera won't do that.

Does anyone know how to take that kind of photo (not sure what the technical name is for the type of photo) with a point and shoot?

If I wanted to buy a camera that would give me that option, can you recommend a good camera that isn't too expensive, but would be more versatile?