Complex sentence: These local currents result in larger changes in the electrical potential between the local extracellular medium and the interior of the recording electrode.That is how the overall recorded signal represents the potential caused by the totall of all local currents on the surface of the electrode.
Split into simpler sentences: These local currents result in larger changes in the electrical potential between the local extracellular medium and the interior of the recording electrode. The overall recorded signal thus represents the potential caused by the sum of all local currents on the surface of the electrode.