Copper (Cu) attracts more electrons than zinc (Zn). When placing a copper plate in contact with zinc, electrons flow from zinc to copper until they start to concentrate and repel each other (polarization). When the copper electrons attraction force is compensated by the electrons repulse force, the electrons stop to flow. Consequently, the direct connection of metals for power supply has very few possible applications (low energy supply).
In contrast, when the two electrodes are dipped in an electrolyte (conductive solution), the electrochemical reaction happens continually. As electrolyte it can be used any acid, alkaline or saline aqueous solution. The electrochemical lemon battery works because the lemon juice is acid and is used as an electrolyte.
Thus, this process of continuous production of electric energy becomes more useful for certain applications. However, as well as it happens for the dry batteries (lithium), these ones have a certain time of life. In the electrodes it happens several chemical reactions that end blocking the electrons transfer from the anode (zinc - from where electrons leave) to the cathode (copper - where electrons arrive).Enjoy and experiment science at home!