By default, your camera is set to front curtain, which means your flash fires at the beginning of the exposure, when the shutter opens.
The rear curtain flash setting let your flash to fire at the end of your exposure, just before the shutter closes. Well, you won’t see a difference at high shutter speeds but you will at slow shutter speeds. Remember what a flash does, it lights up your subject and “freezes” it in time. So if your flash goes off at the beginning of the exposure, you’ll freeze your subject and then the movement for the rest of the exposure will blur right over your “freeze” and it won’t look natural or sharp. If your flash goes off at the end of the exposure, the blur comes first and then you freeze your subject right at the end making it sharp with all the blur “in background” of your frozen subject.
The example of the rear curtain flash, with 1/1.6s handheld :