On-piste skis have an hourglass shape, the sidecut: wider tips and tails and narrower in the middle, underfoot.
The reason is so that when we put them on edge to make a turn, the ski will bend and turn by itself - here is a ski on edge, with and without pressure on it:
This is what makes tipping the skis on edge the best technique for turning, on piste.
The sidecut has a radius - this is the "nominal" arc the ski will make when you put the ski on edge at a "nominal" angle, with a "nominal" pressure. If you put the ski on edge less, it will make a larger arc or skid the turn - this number, the radius, should be marked on the ski, in meters, and here are some categories that you'll find:
If you, on the other hand, put the ski on edge more, with higher speed and bend it more as a result, it will make a tighter turn. The name of the game in performance skiing is bending the skis more.
Talks and sessions:
References and more reading: