This video from The Slow Mo Guys is cool and informative on its own merit, but it's also one of the best illustrations of how and why some crucial flash photography principles work.
Sync Speed
Have you ever seen a dark strip across the lower portion of your photograph when shooting with an external flash? (There's a great example on this page.) Well, that dark strip is a result of shooting above your camera's sync speed - ie, the maximum shutter speed the camera is capable of syncing up an external flash at. The sync speed varies, and and for most SLRs, is usually somewhere between 1/160th and 1/250th of a second (check your manual, or Google your camera model). Some SLRs won't even let you shoot at a shutter speed that exceeds your max sync speed, but if you inadvertently manage to make it happen, you'll know it from the nasty black bar you'll see towards the bottom of the resulting photo. That black bar is actually that same rolling shutter that's clearly visible in the video, casting a shadow as it passes over the sensor.
So what do you do if you want to shoot some high-speed action, using a flash, at a higher shutter speed than your camera can technically work with? Or if you want to shoot with a wide open aperture to get really shallow depth-of-field in lots of bright daylight? Well, many external flashes have high-speed sync mode, which lets you do just that. This flash mode doesn't actually fire a single burst of light; rather, it fires many low-powered bursts of light as the shutter passes over the sensor, thus avoiding casting that shadow. Cool, right?