Not sure what they mean by "prevents mechanical mixing", but the salt bridge in general is responsible for replenishing charges as they migrate throughout the cell, and allowing the flow of electrons to continue. So if you have a KCl salt bridge, the K+ ions migrate toward the cathode as it becomes more negative (gaining e-), and the Cl- ions migrate toward the anode as it becomes more positive (losing e-). This is important because without an outside source of ions (salt bridge), there would be an increase in electrostatic potential, and stop the desired flow of electrons due to the electrochemical potential.