Ion pumps maintain the ion gradient across the membrane in a living organism necessary for coordinated movements in the muscle. In the video, the high sodium content of the soy sauce briefly increases the extracellular concentration of sodium Naturally, these want to diffuse across the membrane to try to reach a state of equilibrium between the inner and outer sections of the membrane. The electrochemical gradient depolarizes the squid neurons, generating action potentials.
In the video, this has less to do with the pumps than it does with the gradient of sodium ions. Still, it's a good illustration of the importance of ions and the pumps which regulate them.