It's related to the springiness of your skis.
If you bend a ski and just let go then it vibrates.
If you lose grip a little and the ski is bent then the tip will spring 'downhill' a bit. This is likely to cause it to come into contact with the snow which then pushes it back 'uphill' into a curve - this happens in quite a snatchy way (and your ski is still not gripping well enough) so it lets go again and the cycle repeats.
Normally the damping in a ski stops this happening - but if you have the right conditions (higher speed, hard surface, tiny bumps - eg a frozen, pisted surface) then your skis will resonate - you can minimise it happening by backing off the edge and applying the pressure smoothly but once your past the point it happens at all it takes is a little bump to set it off.
I suspect that the increased stiffness of race skis changes the resonant frequency. I also wonder if recreational skis have less damping. Not sure