When your thermostat calls for heat, the booster motor (sometimes called a draft inducer) is generally the first thing to start running on your furnace. The function of a booster motor may vary with different furnaces. In some furnaces, it simply brings added air to the combustion chamber. In other furnaces, it may add air as well as help exhaust the combustioned gas up the chimney by either creating a draft or pressurizing the chamber.
If your furnace has sat for awhile, you may find that upon start-up your booster motor doesn’t run. Before ordering a new motor, shut the power off to your furnace and try spinning the motor by hand. It’s common that due to moisture you may have gotten some corrosion inside the motor. Spinning the motor by hand may be all the fixing that’s required.
If your booster motor is running but your furnace isn’t, then you may have issues with the pressure switch or centrifugal switch (whichever your furnace has). Don’t always assume that those switches are bad. The switches may simply be doing their job and have triggered themselves due to other issues (such as a blocked airway).