> Here we demonstrate that neural networks synchronize individual action potentials to create large-amplitude, rhythmic and self-perpetuating ionic waves in the interstitial fluid of the brain

This line is the money shot. An action potential is the variable electrical charge of a neuron, and they maintain that charge by containing a certain concentration of ions relative to the surrounding cerebrospinal fluid. This paper proposes that neurons synchonise their charge state, which forces ions to flow in or out of the neurons in bulk, the movement of these ions causing the cerebrospinal fluid to move around, clearing out the accumulated debris.