How a Windmill Pumps Water

The blades, also known as sails, of the windmill wheel catch the wind which turns the rotor.
The wheel assembly is attached to a hub assembly by long arms. The hub assembly drives a geared mechanism that converts rotary motion to an up-and-down motion.
That up-and-down motion drives a long sucker rod, also known as a pump rod, up and down inside of a pipe in the well.
Attached to the end of the pipe is a cylinder with a sealed plunger going up and down inside that forces the water up the pipe.
Each upstroke pulls water into the cylinder.
On the downstroke, a check valve in the bottom won’t let the water be pushed out, so the water is forced up the pipe with the next upstroke.