That line is used for a continuous run unloader setup. These are used on gasoline engined compressors as well as larger electric units as a way of increasing duty cycle. I have a Dayton compressor that has an unloader, it is great for long sessions using the blast cabinet. It works by air pressure, sending pressure into the lines activates a piston to hold the intake valves on all the cylinders open, stopping the compressing action (the cylinders now breathe in and out of the intakes) while the pump still runs. This allows a gas engine to continue running, or in the case of electrics, the pump still runs, receiving cooling air from the flywheel fan. This is very useful for heavy continuous use.
The compressor setup needs a "pilot valve" that is preset to just below shut-off pressure, usually about 5 psi. This valve opens at the set pressure, sending air to the uloaders, when the tank pressure drops by about 10psi, the valve closes tank pressure and vents the unloader side to the atmosphere, releasing the pistons holing the intake valves open, resuming compressor function. Some 2-stage compressors have an interstage valve that opens with the unloaders, reliving pressure between the first and second stages (where the intercooler resides) to allow the second stage cylinder(s) to breathe freely when running unloaded.