These flash sync problems only occur because we have focal plane shutters in our DSLR cameras. Before the SLR was invented, shutters were in the lens and were a little leaf shutter assembly which experienced little stress at all.
When they invented the SLR the lens had to be open all the time as it's also the viewfinder, so the shutter had to be moved, and they put it right at the back of the camera where it lies just in front of the film or sensor which are actually in the focal plane, but a focal plane shutter is in fact just in front of the focal plane.
Focal plane shutters consist of two metal blinds or curtains. When we use flash, and press the shutter, the first curtain travels upwards, completely exposing the sensor, the flash fires (recording the whole scene because the whole sensor is uncovered) then the second curtain travels upwards covering the sensor.
The camera recocking/winding mechanism then pulls the second curtain back to it's original position dragging the first curtain with it ready for the next shot.
The flash sync speed problems arise as the shutter speed starts to get faster. It varies from one manufacturer to another, but usually the max sync speed is around 1/200th or 1/250th of a second. The reason for this is that there's a limit to how fast they can make those blinds travel upwards across the sensor, and it's already a big, quite violent mechanism with a limited life span, so it's undesirable make it any faster anyway.
The way they get round the problem is that at shutter speeds faster than the max sync speed of (say) 1/200th, is that just after the first curtain starts to uncover the sensor, the second curtain starts it's travel behind it, creating a moving slit across the sensor which exposes the sensor for the desired time, but incrementally - the whole sensor gets the right exposure but not all that the same time.
The faster the shutter speed, the narrower that slit gets to give the shorter exposures right up to 1/8000th of a second.
If you use flash at a shutter speed higher than the maximum flash sync speed of the camera, then when the flash fires it will only record the part of he scene which corresponds to the width of the moving slit at that time.
Hi Speed Sync
Isn't true sync at all, the way it works is that the flash puts out a continuous pulse of small flashes ( like a string of beads) throughout the duration of that moving slit so the whole scene is recorded by the flash.
It's best used at short distances and large apertures as it obviously puts a huge load on the flashgun which it struggles to meet as the aperture gets smaller.
Hope that helps.