It is the usual lift method for lower-rate oil wells on land. On the upstroke the plunger lifts the fluid above it and, through a travelling valve and a standing valve, fills from below. Pump-off (a pump that empties the barrel faster than the well fills it), gas interference, and rod fatigue are the everyday problems.
Rod stretch in a deep well, and rod wear in a crooked well, limit where it is a good choice. A progressing-cavity pump or an electric submersible pump takes over when the rate, the depth, or the deviation no longer suits rods. The surface unit rocking at the wellhead is the visible part; the pump that moves the oil is downhole.