Say we have a scalar function t. If we started a point A and move a small distance, the function will change by an amount given by the gradient of that function along that distance. If we now move the point B in the same manner and add all these small changes together, we've effectively taken the line integral of the gradient of t from A to B along some path. But since we've only calculated the relative change from A to B, we might as well look at the difference between the values of the scalar function at the start and end points. This is the gradient theorem. Since the right side of this equation is independent of the path taken, evidently the line integral on the left hand side is also independent of the path taken from A to B. And in the case if you end up where you start, the close line integral must be equal to zero. The gradient theorem plays an important role in the electrical potential and other Maxwell equations.