The "Flash Synch speed" is a measure of how fast the shutter goes.
For slow shutter speeds the first curtain opens fully, and then the correct time later the second curtain comes across to close the window. For faster shutter speeds the first curtain starts and then the second curtain follows it, with the gap between them being a horizontal slit that moves down the frame.
In order to expose properly with a flash, the whole frame has to be open, so that neither the top nor bottom is put in the dark as the (very short) flash pulse fires, so the flash has to be synchronised to fire when the first curtain has fully opened, but the second curtain has not yet started to move across.
The fastest speed this happens is the synch speed, and is typically 1/250s, or about 3 milliseconds.
For faster shutter speeds trying to capture really fast movement, like a small birds wings beating, the 3ms time is not enough to freeze the motion properly, and it looks like the wing is bent.