its all about the aperture youre using and how close you are to your subject / how far the background is from your subject. what camera and lenses are you using ?
Well, since it looks like you're using a fuji finepix camera, you want to shoot your phoyos in A mode (on the dial on top of your camera). This lets you shoot your photos using manual aperture settings. The lower the number, the wider your aperture. I think on fuji the lowest you mat be able to go is f2.8. this will give your background a blur. play around with your aperture settings and youll see how this works on your depth of field.
To add to TJ's post, you want to get nice and close to your subject so the background is as blurry as it can be - this is easier with f/2.8 than with higher f-numbers. Have a play and see what happens. :)