This came up tangentially in another question. A camera's sync speed is the fastest shutter speed for which the first shutter fully opens before the second shutter begins to close. This is important because if the shutter is never fully open, there is no moment for which the flash can expose the entire image.
While the advent of technologies like HSS(High Speed Sync) have allowed taking flash photos beyond the sync speed, they result in much less available flash power. What are the limiting factors that contribute to cameras not having a faster sync speed?