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That's gradient descent. The name is just plain description: a gradient is the slope of the ground at any point, meaning how steep it is and which way it tilts. Descent means going down. So gradient descent means: find the slope, step downward, repeat.
At each step, check which direction the ground slopes downward and take a small step that way. Then check again. Repeat, thousands of times, across millions of examples. The weights gradually settle toward a valley, a combination that performs well.
The size of each step matters. Too large and you overshoot the valley entirely. Too small and training takes forever. The step size is called the learning rate, and finding the right one is part of the craft of building networks.
Backpropagation tells you which direction is downhill. Gradient descent tells you how to walk.