The limitation has to do with synchronizing the length of the exposure with the length of the flash burst. The flash does not go off immediately...it occurs a fraction of a moment after the shutter has opened, and the burst only lasts a fraction of the time the shutter is open. This is necessary to produce a proper exposure when using a full-powered flash due to the way the shutter itself works. The maximum shutter speed that can be achieved at is 1/200th or 1/250th of a second most of the time. With more precise logic and shutter timing, you can achieve 1/500th of a second flash sync, however thats more difficult (and therefor expensive) to do, which is why its relegated to only top of the line pro-grade cameras. This ensures that the front shutter curtain is fully open before the flash pulse is set off, and that it stays open long enough for the effects of flash to properly light the scene and allow correct exposure before the second curtain closes.
There is also an alternative approach to flash, called high-speed flash sync. This allows flash to be used at any shutter speed. The difference between high speed flash sync and normal flash sync is that at shutter speeds above about 1/500th of a second, the second curtain starts to close before the first curtain is fully open...a shutter "gap" transitions across the sensor. High speed flash sync uses a lower-powered flash pulse set off multiple times in rapid succession to ensure that the scene is properly lit for each part of the sensor as that shutter gap moves across it. High speed flash sync is generally not as good as standard flash, and in most cases it should not be needed...but in a pinch it can do the job.