Confusing description of torsion of a curve? In my textbook (by do Carmo) and both in wikipedia.
There are descriptions of what a torsion is, and both of them says it is a measure of "how fast a curve twists out of the plane of curvature"
I am aware of the definition of torsion which is the magnitude of the derivative of the binomial vector, but I fail to see how this describes "how fast the curve is twisting out of the plane" or "pulling out of the plane".
If we are talking about how fast the curve is traveling outside of its osculating plane, then this makes absolutely no sense to me at all, since the tangent vector is on the osculating plane.

When a curve is planar, all osculating planes are equal.
When it is non planar, i.e. has some torsion, the osculating planes stop staying parallel when you move along the curve, and this change of direction is reflected by the binormal.

"Infinitesimal" insight:
Imagine the curve discretized with a fixed step.
Two successive points define a line, which is the tangent.
Three successive points define a plane, which is the osculating plane.
A fourth point can deviate from the plane and show the torsion. In other words, two triples of successive points will define two distinct planes and the angle between them corresponds to the torsion.
