What does the gradient function mean?

The gradient function gives the slope of a function at any single point on its curve.

This video gives a brief explanation:

For instance, if the curve is increasing (i.e. increasing in value as we move from left to right along the graph), then the sign of the gradient function will be positive. Or if the curve has a horizontal slope at a particular point (a "stationary point"), then the gradient function will be equal to zero at that particular point.