This synchronisation problem is caused by the shutter design. A modern electronic shutter is usually made from fabulously thin, but strong, metal blades that open and close by rolling a two-panel 'blind', or curtain, over the frame opening. Press the shutter button and the curtain opens fully, waits for the appropriate shutter delay time, then a second curtain is dragged, in the same direction as the first, across the aperture and therefore 'finishes' the exposure.
For shutter speeds slower than 1/200s, the aperture fully opens before the second curtain is dragged across it to finish the exposure. But if you want to use flash with faster shutter speeds, the camera has to move the second curtain before the first curtain has finished opening to achieve a very fast shutter speed - like 1/4000s.
At 1/4000s, for example, the second curtain is so close behind the first curtain that it resembles just a thin slit travelling vertically across the sensor. So, if the flash is fired in combination with a fast shutter speed, it will only illuminate part of the sensor, producing a horizontally-flashed stripe through the frame while the rest of the exposure has no flash. It's a disaster.
To prevent this happening, manufacturers now place a top limit on flash sync shutter speed - this varies slightly depending on the manufacturer, but it's usually 1/200s - to find out either check your camera's tech specs, or place the camera into Manual metering mode, pop up the flash and try to increase the shutter speed - it will not go past the maximum allowable - the flash sync speed.
The trick to getting over this technical shortcoming is to use the speedlight's special High Speed Flash Mode (called FP Mode on Nikon Speedlights). This very neatly gets round the problem of a single, quick flash of light (typically at 1/1000s). The speedlight actually fires a burst of many thousands of flashes in a very short space of time, creating - effectively - one single, but much longer burst of light that covers the time it takes to move the shutter curtains across the sensor. This all happens, well, in a flash, to our eyes with the amazing result that in this mode, we can shoot at any fast shutter speed, from 1/200s up to and including 1/8000s.
This function provides photographers with the benefit of being able to shoot at very wide apertures (i.e. f1.4) for an extreme shallow depth of field, in bright light. Without this mode, you'd have to shoot at 1/200s at f22, producing a good depth of field, which is not what we want...
(One thing to bear in mind before you start shooting is that any type of flash synchronisation, on-, or in particular off-camera, is reliant on having the right gear. If you plan on working with multiple flash units, it really pays to have the same gear. Mixing and matching different speedlights with non-standard triggers can prevent you from using all the speedlight's features, in particular its high speed flash sync mode).