I learned about this while studying neurology. As an EE I had to keep reminding myself that in biology there are several kinds of current flows, and they do not include the usual kind (electron flow) that I'm already familiar with. They include both positive (Na+, K+, Ca++, Mg++) and negative (Cl-) ion flows. Because of the non-equilibrium maintained by the pumps, these ions usually flow spontaneously when a channel opens for them, even when they flow "uphill" against the charge gradient. E.g., when a K+ channel opens, K+ will flow out of the cell and make the inside even more negatively charged because there's a much higher concentration of K+ inside than outside because of the pumps.
I did not realize right away that these ion pumps exist in every cell, not just neurons, so they must have evolved very early for mechanisms other than making nerves work. And true to the way evolution works like a third world junkyard, repurposing one mechanism for completely different purposes, some organisms have evolved special nerve cells that they use as offensive weapons, e.g., the electric eel. Fascinating stuff.