Drop a ball on a hilly landscape and it rolls downhill, always in the steepest direction, until it settles in a valley. Gradient descent does the same thing to find a low point on a curve: check which way is downhill from where you stand, take a small step that way, then check again.

Each step uses only local information: the slope right under your feet, never the whole landscape. Repeat enough small steps and you end up at the bottom, the same way a ball finds the lowest point of a bowl without ever seeing the whole bowl at once.