A condensing furnace is a high-efficiency gas furnace that adds a second heat exchanger to wring extra heat out of the exhaust. It cools the flue gases so far that the water vapor in them condenses into liquid — recovering heat that an older furnace sends up the chimney. That second exchanger is what lifts efficiency, measured as AFUE, into the 90% to 98.5% range, versus about 80% to 83% for a conventional 'non-condensing' furnace.
Two things follow from condensing the exhaust. First, the cooled flue gases are no longer hot enough to need a metal chimney, so a condensing furnace vents through PVC or CPVC plastic pipe, usually out a sidewall. Second, the unit constantly produces a small stream of mildly acidic condensate that has to drain away through a condensate trap and drain line.
That drain is the part homeowners most often meet by surprise. Algae, sediment, and slime clog the trap, or a drain line run through an unconditioned space freezes. When water backs up, a float or pressure switch shuts the furnace down to keep acidic water from damaging it — so a $0 clog presents as a dead, no-heat furnace that looks like a major failure. Clearing the trap and drain is a routine, inexpensive fix, and a recurring clog is a sign the condensate path needs attention rather than a reason to replace the furnace. If a condensing furnace 'won't turn on,' the condensate system is one of the first things a good technician checks.