Way back when I was in first grade--for the fifth time--they called those things thermocouples. About the time I graduated from the 6th grade and got ready to go into the Army, they changed the name to flame sensor. I guess that this was because nobody could spell thermocouple including me and that really wasn't the job that they did. The term flame sensor is more accurate.
If you get a good service tech, he'll tell you what the problem was and clean the burner area and do some of the other maintenance you should have done annually. He could just hand you a bill with the part number and the price for the part being the same 6 digit figure. He could tell you that "It was that thingie--you know the one that always goes bad." Chances are that he'll tell you that you have a bad flame sensor. He will replace it and maybe show you how to do it. Mine costs about $8 for a new one and I usually buy a spare to have on hand, just in case.
There are a lot of parts in a lot of furnaces. Gas valves and other parts may need to be replaced too. Just because I'm making a guess from miles away is no substitute for a qualified tech there to diagnose the problem and fix it.