Question

what actually a GRADIENT VECTOR is?

Answer 1

It is a vector containing all the rate of changes of the inputs of a function. It basically tells you how a function value will change given a change in any of its inputs.

Answer 2

This vector points in the direction of the most rapid rise in the rate of change of the variable. Think of standing on the side of a mountain. Pick the shortest route (steepest) route to the peak of the mountain. This is the gradient vector AT THIS POINT IN SPACE. As you continue to climb, the steepest direction continuously changes, because the mountain surface in not flat. These collective directions, plotted on a map, comprise a "gradient field".