In order to answer to your question, let me take as an example the juice from lemon, which is an acid. Lemon juice contains something called electrolytes. An electrolyte is a substance (like an acid) that when dissolved (as in water) conducts an electric current.

The acid can't produce electricity by itself, but it can allow two different metals to react with each other. When these two different metals react with each other, one metal gains electrons, while the other metal loses electrons.

In order to produce the electricity from an acidic fruit (like lemon), you need two different pieces of metal such as Zn (Zinc) and Cu (Copper) and a conducting wire like Cu as well. Remember that the acid inside the lemon juice are chemicals and has chemical energy and it can serve as the electrolyte. The two pieces of metal which are in contact with the acid, are called electrodes. One of the electrodes will gain electrons and the other will lose electrons. When you connect the two electrodes, the electrons will flow along the conducting wire, then you get the electricity.

This experiment works well with lemon juice, but not all fruits contain the same amount of acid. I have never tried another fruit, but you could experiment for instance with grapefruit. What you definitely need is an acidic fruit as lemon.