Original: Typically, a fast shutter speed will require a larger aperture to ensure sufficient light exposure, and a slow shutter speed will require a smaller aperture to avoid excessive exposure.
Simplified: Typically, a fast shutter speed will not let much light in (meaning the picture could come out too dark), so the photographer will use a larger aperture to correct for this. A slow shutter speed will need a smaller aperture to stop the picture coming out too bright.