The fan limit switch is a control that is in charge of making sure your furnace's blower assembly turns on and off when it should. This prevents your furnace from circulating cold air throughout your home before the burner heats up, and from blowing hot air after the temperature has reached the setpoint on your thermostat. The fan limit switch is also important if your furnace overheats because it shuts down the burner before damage can occur.
The fan limit switch senses temperature through a bimetallic spring -- sometimes called a bimetallic coil -- which is inserted into your furnace's warm air plenum. As the air inside the plenum heats up, the spring expands, turning a gear that rotates the fan limit control dial. As the control dial rotates, it operates electrical contacts inside the switch to turn the fan on and off.
In most cases, the fan limit switch looks like a round, silver, button-like switch. This is referred to as a snap disc limit switch. Some models have a long metal sensor instead, or a mounting arm with a snap disc attached to it. Location varies depending on what brand and model furnace you own, but the fan limit switch is generally on or somewhere near the circulator blower.
The fan limit switch is an essential part of any gas furnace, and your system should not be run without it. A technician may temporarily circumvent the fan limit to test its effectiveness, but running the furnace without this switch puts you at risk for overheating. It could also damage your furnace and home and cause potential injury to yourself and others.