HSS allows the flash to sync at shutter speeds faster than the sync speed of the camera (typically at or slower than 1/200 or 1/250). It does this by firing a pulse of light instead of a single shot of light; the series of pulses requires the flash to fire at a lower power per pulse so the overall effect of the flash is far less than normal.
HSS is ideal for fill flash where the light is lifting shadows, but not contributing the main exposure of the shot in a strong manner (unless, of course, you have a lot of flash units). It also becomes rather tricky for action because any fast motion is going to show blur as it catches the haze in the series of flash shots instead of a single action stopping pulse of light.
In theory if you are controlling the shutter speed directly (shutter priority - manual mode) you could remain in HSS as it is only needed at shutter speeds faster than the cameras sync speed. If, however, you're letting the camera control the shutter speed it might well go slower than idea, since the camera meters without the flash (TTL and auto metering tend to work best for the flash as a fill flash light source).
It strikes me that, without the context of the video, the person in the video likely only uses flash for fill lighting or they are directly controlling the shutter speed for their shoots.