When the plunger moves up the cylinder, a low pressure is created in the cylinder. The fluids is drawn by the low pressure by means of non return valves in the inlet of the pump.
When the plunger moves down, the increased pressure closes in the non-return valves in the inlet. The liquid is pressurized as the plunger moves downwards. This high pressure opens the outlet valve and the liquid is ejected at high pressure.
Plunger Pumps can be used at high pressure because of their robust and simple design.