The second derivative is what you get when you differentiate the derivative.
The second derivative can be used as an easier way of determining the nature of stationary points.
A stationary point on a curve occurs when dy/dx = 0. Once you have estabished where there is a stationary point, the type of stationary point (maximum, minimum or point of inflexion) can be determined using the second derivative.
If d²y is positive, then it is a minimum point.
If d²y is negative, then it is a maximum point.
If d²y is zero, then it could be a max, a min or a point of inflexion.
If d²y/dx² = 0, you must test the values of dy/dx either side of the stationary point, as before.