Electrical neutrality between electrodes of galvanic cell: why is it necessary for current flow?
A galvanic cell is driven by two reactions that occur, one at each of the electrodes. Each reaction creates a potential difference between the electrode and the surrounding electrolyte. The salt bridge functions as a conductor that keeps the electrolyte at both electrodes at the same voltage, which then forces the entire potential difference to appear across the external load.

Without the bridge, there would be no voltage across the load, and the entire potential difference would be between the two isolated batches of electrolyte. However, the bridge must not conduct electrons, because that would short out the cell internally, and the reactions would proceed without limit until the reactants were consumed.