This object is an ancient water pump invented by the Greek Ktesibios but then later adapted by the Romans in the third century. The Romans then changed the pump to have two cylinders instead of one that can still be used by one person. The pump would be placed in water to draw the water into its cylinders forcing the water through a central outlet connected to a vertical pipe. The pump was mostly used to fight fires and could be used on ships as well to fight ship fires.
Ancient Roman water pump, a sophisticated artifact of mechanical engineering.
Roman pump found in Spain
Pieces of the pump
Ctesibius' Pump, from Roman mine, Valverde Huelva, Spain
Piston pumps are a roman invention. They date back to 250BC. Authors like Vitruv and Heron of Alexandria give descriptions of pumps and other mechanisms whose function is based on cylinders and pistons.
Classic sucktion pumps only work, if water is to be pumped up less than approx. 10m (=33ft). In ancient times, this effect was explained by Aristotle's horror vacui i.e. nature abhors vacuum. It took until the mid-seventeenth century until Evangelista Torricelli, a pupil of Galileo Galilei found the correct explanation.