A "shutter trip" commences with the opening of the first shutter curtain to begin exposing the sensor, and concludes with the closing of the second shutter curtain to cover the sensor again. These shutter curtains can only move so fast, the time it takes them to go from top to bottom is roughly on the order of the camera's sync speed (e.g. 1/200). For shutter speeds faster than this, the second curtain begins closing the shutter before the first curtain has fully opened; in other words, the sensor is exposed by an open "slit" between the first and second curtains traveling vertically along the frame. The shorter the exposure, the narrower this slit is; for instance at 1/2000 sec you'd expect this slit to be about 1/10 the height of the sensor, moving vertically along the frame to expose the sensor along its full height.
In normal flash photography, the shutter must be fully open for a time, and the flash is "fired" during that time, either just after the first curtain has fully opened (i.e. near the beginning of the exposure) or else just before the second curtain begins to close (i.e. near the end of the exposure). If the flash was fired when the shutter was not fully open, e.g. when the first curtain was only half way open, then part of the sensor would be blocked for the duration of flash, which is extremely short. So normal flash doesn't work at speeds faster than the sync speed, which necessarily imply the sensor being exposed by a partial "slit" opening between the shutter curtains, with the shutter never fully open.
In high speed sync, the flash releases its stored-up energy gradually over a longer time, instead of all at once, e.g. by pulsing the flash in little bursts. So in a very fast exposure, where the sensor is exposed by a small "slit" between the first and second curtains, the flash lasts for the entire duration (roughly 1/200 second), continually flashing and "exposing" the sensor as the slit moves along the height of the sensor.
The downside is that some of the flash's energy is now uselessly bounced off the closed shutter. For instance, for a 1/400 shutter speed, you'd expect the "slit" to be about half the height of the sensor, and thus any flash energy released at any point in time can reach no more than half the sensor, the other half being wasted, blocked by the closed curtains. The faster the shutter speed, the smaller the slit, and the lower the percentage of flash energy that gets "used".
So high-speed sync uses flash energy less efficiently than normal flash, and that efficiency drops rapidly as shutter speeds get shorter. This reduces flash range, increases battery drain, and increases the time needed to allow the flash to recharge, relative to normal flash. This downside is why a camera/flash typically requires the photographer to intentionally enable this functionality, to say "yeah, I know, but I really want HS any way".
-harry