X-sync is the lowest shutter speed during which the shutter is entirely open at some time, and thus allows use of flash. (You don't want it to light just top half of frame.)
X-sync differences don't play that much role about stopping action (flash pulse duration is around 1/1000 anyway), but rather eliminating ambient (or overpowering sun, if you want) with flash in photos when you have both kinds of light.
If you have a flash-lit portrait outside, you usually want to have the surrounding landscape a bit darker than the person. Now, if you use a full power of your flash, and get proper exposure of foreground at f/8 and ISO 100, out might even get background overexposed at 1/200 sec if it's sunny day. Being able to go to 1/500 might make the shot possible, or allow you to raise ISO to 200 and save some flash power to get faster recycle times.
Sometimes you can kind of "cheat" by using high speed sync which fires the flash multiple times to cover all parts of the frame. This doesn't really help in this situation as it eats flash power you need to have foreground exposed properly.