The first idea of curvature(Fig.1) is that
when you walk 1 meter, how much you fall or rise.
In this idea, the curvature of a line is zero.
In Fig.1 [A] and [B], we can understand that
the longer the radius of a circle is, the shorter the distance of fall is.
When the radius is shorter than 1 meter, we cannot define curvature(Fig.1 [C]).
The second idea of curvature(Fig.2) is that
when you walk from the point P to the point Q (meaning the distance, Δs),
we could value at the angle between the two vectors a and b for Δs,
where the vector a is the tangent at the point P and the vector b is the tangent at the point Q.