The furnace blower motor drives the fan that provides air movement for the furnace. Typically, the furnace's element heats the heat exchanger until it reaches optimum temperature, then the blower motor engages to push air through the exchanger. This warms the air and distributes it throughout the home.
In addition to providing forced air for the furnace, most furnace blowers double as air handlers for the air conditioning system as well. Central air conditioning units are often simply connected directly to the furnace, with the same air passing through both the heat exchanger and the evaporator coil. With one unit or the other turned off, the remaining one can heat or cool as necessary.
The furnace blower is also where air filters are generally installed in a central heating or cooling system. This traps dust before it can adhere to surfaces inside the furnace, where it could potentially interfere with the blower's ability to turn. Since the air handler moves such a large volume of air, a high-quality air filter mounted before the blower motor can serve to purify the air inside the entire home at once. Filters should be replaced regularly to prevent dust build-up that can reduce the amount of air flowing through the system, forcing the blower motor to work harder and potentially leading to a burnout.