Slow-sync flash mode: 1/4 sec. shutter speed
Standard flash mode: 1/250 sec. shutter speed
In the image taken using standard flash mode the shutter speed was 1/250 second, so the subject is well lit but the background is dark. In the slow-sync image the subject was correctly exposed by the short flash pulse, and the slower 1/4 second shutter speed exposed the background properly as well.
In slow-sync mode the flash fires, exposing the subject, and then rather than closing immediately the shutter remains open for long enough to expose the background as well. This gives you well-balanced images in which both the subject and background are properly exposed.