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. This number, the radius, should be marked on the ski, in meters, and here are some categories that you'll find:
This printed radius of the sidecut is more of an FYI, relaying some basic information about the ski's intended purpose and how the ski will behave. The reality is that you'll rarely get the same radius turn.
If you put the ski on edge more, at bigger angles than the nominal angle for the "printed radius", with usually higher speed, it will bend more as a result and it will make a tighter turn. The name of the game in performance skiing is bending the skis more.
The aim of the skiers should be to be able to control the radius of the turns they make and be able to make at least sidecut turns, i.e. make the ski bend at least with the sidecut radius.
That is achieved by tipping the skis at the appropriate (bigger) angle and balancing on it, to get it to bend sufficiently to make the shorter radius turn. This requires better tipping and counterbalancing as well as counteraction.
Talks and sessions:
References and more reading: