Curvature measures how straight a curve is at a point. If curvature is zero everywhere, the curve is a straight line.
If x = t, curvature is ; for small y´, this is approximately the second derivative.
The square of the curvature can be (sometimes) approximated by x´´ 2 + y´´ 2.
The less is the curvature, the “nicer” is the curve.