Its a vent for the expansion tank. This tank allows the water in the stainless tank to expand, but also allows the hot water in the line between the dispenser and the tank to drain back down when you turn off the dispenser so you don't get a plug of cold water when you first open the valve.
When you open the valve on the counter, pressurized cold water flows through the left inlet and into the bottom of the tank through a tube inside the tank. This forces hot water out the center outlet. When you release the valve, the hot water in the line between the dispenser and tank gravity feeds back down and fills the expansion tank through the gray tube. Where the 1/8" tube tees into the left inlet, there is a venturi, which, when pressurized water flows through the inlet, it creates a vacuum on the 1/8" line, sucking water out of the expansion tank and back into the stainless tank. Once the water in the expansion tank is sucked out, a floating ball comes down and blocks the hole in the bottom of the expansion tank, which prevents air from being sucked into the tank, which would blow bubbles and cause the dispenser to sputter.