What is AirTTL technology?
TTL stands for Through The Lens metering.
Most of the time when using off camera flash the lights are set manually, but to speed things up Profoto built AirTTL into their newer flash units. This lets the Air Remote "speak" to the cameras light meter to figure out how bright the lights are and adjust them.
By firing a pre-flash pulse, the camera reads the light in the scene, then the AirTTL remote adjusts each light's output according to your preference, and finally the exposure occurs with the correct flash power. This can be very helpful if you are moving around frequently, or working in changing lighting conditions and manually setting flash power is not practical.
What is HSS technology?
HSS stands for High Speed Sync.
Cameras that do not have leaf shutters - that is most DSLR cameras - cannot synchronise with flash at faster shutter speeds, above around 250th/s, as the shutter would block part of the sensor during the flash pulse. This results in black bands covering much of the image.
To address this and give photographer more creative freedom Profoto developed a way to have their flash pulse over the entire time the shutter opens. So instead of flashing once the light pulses multiple times very very fast, momentarily turning a flash into a constant light source.
So with HSS enabled on a Profoto flash you can shoot at much faster shutter speeds (to darken the ambient exposure) and illuminate your subject correctly.