The problem isn't simply that the background image is "big," but that it's designed to match up with the markup at a specific size. The space between the visual "edges" (where the blue ribbon folds and there's a drop shadow) on the image is 1180px wide: this fits with the div's width of 1180px, so that your primary content stays contained within the middle of the image. If you change the div's width to 100%, then your content is allowed to outgrow the 1180px visual area of the background image.

You could eliminate the background image, but it seems like that would be removing much of the design. You might want to look for a different template with what's often called a "liquid layout" - these are designed with percentage dimensions to fit any resolution.