Between the fins = the water channels. The fin plate is a comb of 271 thin copper walls standing on the baseplate. Each fin is 0.1 mm thick, with a 0.1 mm gap to the next one. The water flows through those gaps, the narrow slots between neighbouring fins, so the baseline has 270 tiny channels side by side, each 0.1 mm wide and 2 mm tall. The gasket presses on the fin tips from above and closes the top of each channel.
A slice across the fins, looking along the flow. Only 22 of the 271 fins are drawn, and the horizontal scale is stretched so the 0.1 mm features are visible. The water (light blue) fills every gap. Heat goes up from the chip, through the TIM and baseplate, into the fin walls, and out into the water sliding past them.