I don't have the manual for my furnace, and the terminals are labeled C W R G and Y. The internet generally refers to Y as Cooling or Compressor. So what does Y do on my furnace?
Y turns the fan on
Gas furnaces are fairly autonomous with regards to how they handle controlling their blower (vs. electrically heated air handlers, which require the thermostat to manage the blower for them). This is to provide for proper thermal management of the heat exchanger, and also for historical backward compatibility with two-wire heating-only thermostats such as those found in old buildings.
As a result of this, the furnace needs to know when the air conditioner is engaged in order to run the blower so that the cool air can circulate (and the indoor coil doesn't freeze, for that matter). This is done by having a connection from the Y signal to the furnace fan relay (either physically on older furnaces, or logically on newer ones with a control board), so that the fan comes on (on cooling speed if a multispeed or ECM blower is present) whenever cooling is called for.