τ = -N . B'
is called the "torsion", and is equal to the rate of change of the osculating plane. You can think of it as the amount by which the curve is twisting. A curve which twists the same amount (e.g. a helix) has constant torsion.
Given two single-valued functions κ(s) and τ(s) given for s > 0, there exists exactly one space curve, determined except for orientation and absolute position, for which s is the arc length, κ is the curvature and τ is the torsion. This is known as the fundamental theorem of space curves.
And if you thought that was remarkable... the whole thing generalises to higher dimensions and non-Euclidean spaces!
You've just opened a door to the wonderful world of differential geometry. You also may just have discovered your graduate school major. Or possibly not.
Answer to the additional details question:
I mean it can't be the zero vector. If |r'(t)| = 0, then r'(t)/|r'(t)| is (obviously) undefined.