The diagram shows a modern, simple, manually operated vacuum pump.
Each time the piston is at the bottom of the cylinder, air from the vessel to be evacuated expands into the chamber above the piston. On each upstroke, air above the piston is pushed through the upper valve. The oil around the piston acts as a lubricant and a seal, and fills the dead the space between piston and valve at the top of the stroke so that all the air there is expelled.