When shooting with a subject in low light situations you generally have two options; either to shoot with a flash or to shoot with a slow shutter speed.
Flash usually leaves you with a sharp, but brightly lit up subject while losing a lot of the background ambient (color and detail). A slow shutter speed requires the subject and photographer to make no movements, or the result will be a blurry image.
Slow Sync Flash is a function found on many cameras that tells your camera to shoot with both a longer shutter speed as well as firing the flash. This means you get the best of both worlds above and can both get a relatively sharp shot of your main subject as well as get some ambient light from the background and foreground.