In mathematics (usually covered in study of The Calculus or Physics), the derivative of the derivative. I.E.: Take the derivative of a function, and then take the derivative of that derivative. This describes the rate of change of the rate of change (or slope of the slope) of the original function.

Example:

Function: F(X) = X^3 + X^2 + X
Derivative: F`(X) = 3X^2 + 2X + 1
Double Deriv.: F``(x) = 6X + 2

The double derivative is most often used to find the acceleration of an object or particle.