# Interpretation of Curvature formula for a parametric curve

Given $S(t) = (x(t), y(t))$, the curvature at any point on S is given by below formula:

$$K = \dfrac{S'(t) \times S''(t)}{|S'(t)|^{3/2}}$$

Where $S'(t)$ is the first order derivative of $S(t)$ and $S''(t)$ is the second order derivative of $S(t).$

1. I know that the first order derivative gives the tangent vector function to the curve, but How do i interpret the second order derivative of a parametric curve?

2. In the above formula for curvature, how does more "perpendicular-ness" between $S'(t)$ and $S''(t)$ increases the curvature of the curve?