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It means the thermostat is calling for heat but there is a furnace malfunction. Usually an open limit circuit. This can be caused by a dirty filter among other things.
This doesn't sound like a themrostat problem. If the filter is clean then about the only other thing you can try is resetting the rollout switch(es) (see attached pic for typical). They are located just outside the burner chamber. Turn off the power then press the small button between the 2 leads to reset it. If it clicks you have reset it and the unit will fire up when you turn the power back on with any luck. If it doesn't click it wasn't tripped.
Check to be sure there isn't more than one by tracing the leads connected to the switch. If that doesn't work then it's time to call in a pro.