Copper vessel is tarnished due to copper oxide layer formed on its surface .
Copper oxide is basic in nature. The green coating on copper vessels is due to the formation of basic copper carbonate formed by the attack of O2, CO2 and moisture of the air on the copper vessel.
Lemon is acidic. Thus, on rubbing the tarnished copper vessel with lemon, the basic copper oxide or copper carbonate reacts with the acid (citric acid) present in the lemon to form a salt which is washed away with water.