This is important because it brings full attention to the object in the picture, with your eye out of focus of the background, in the example with the bird and a blurred green backgound.
Background simplified is important because it draws focus to the object but still includes a background, unlike no background. This picture still is focused on the main object (the man) but still includes a background that doesn't take away from the object.
No background is important because it draws complete focus to the main object in the photo. This picture shows it because there is nothing but white behind the pretty seagull, drawing your focus to the pretty seagull.