Fan relays are used for a variety of applications on various central units. On gas units the fan must blow slower in heat mode than in cooling mode. How do they do it? With a fan relay. A Fan center is mounted near the innards of the furnace to control the fan speed. It has a transformer to power up the thermostat and a fan relay mounted on it to control the fan speeds.
Mounted smack dab on top of that fan center is a relay. The relay is set up to where it allows for the furnace speed (Red wire on fan) to be on all the time for heat. When the cooling portion comes on you need to have that fan going full blast on high (Black wire to that fan motor). It is done through the that relay which shifts the fan from slow to fast,
Here is better look at that relay after it is yanked out of the fan center. As you can see it has a coil mounted on it. The coil is a 24 volt one that is controlled by the thermostat. When cooling is called for this puppy shifts from low speed for furnace, to high speed for AC.
These relays also come in a variety of ways. Here is another common fan relay called a peanut:
It also works on 24 volts and does basically the same thing as the other one above. It is good to know how to ID these because a lot of times they will fail. It is a simple repair, IF you know what you are looking for.