The dowsing rods do indeed move, but not in response to anything underground. They are simply responding to the random movements of the person holding the rods. The rods are typically held in a position of unstable equilibrium, so that a small movement gets amplified into a big movement.

Does water divining actually work?

There is no evidence that divining, which relies on the spontaneous twitching of sticks held in human hands, can accurately detect anything beneath the ground.

Why does water dowsing work?

The natural explanation of "successful" water dowsing is that in many areas underground water is so prevalent close to the land surface that it would be hard to drill a well and not find water. In a region of adequate rainfall and favorable geology, it is difficult not to drill and find water!