Two Stage Gas Furnaces
The two-stage gas furnace changes the burn rate of the natural gas, or the amount of BTU's (British Thermal Units - is a measurement of heat energy) of heat generated. Many also will change the speed of the blower fan, setting it lower for the first stage and higher for the second stage of heating blowing less and more air as required based on the BTU's of heat.
So what's the advantage?
Well the real advantage is really in comfort and not in energy savings, granted there is some energy savings if the blower changes to a lower speed (not all 2 stage units do this) and this is due to the fact that all BTU's are treated the same.
In other words it will take the same amount of BTU's to heat your home at 40 degrees outside no matter how neat of a furnace or system you might have and it will always take more of those BTU's to heat your home at 30 degrees than it did at 40 degrees. That amount pretty much stays exactly the same at each specific temperature unless you add another source of heat or take it away, that is simply a fact.
The idea of the two stages is to allow the furnace to actually run on a lower amount of BTU's and run longer keeping you home more comfortable by decreasing the temperature swings from when the system goes off to when the system comes back on, other than the small savings in energy that is pretty much it. Are they worth it, well yes, many customers love them because they do work and they do keep the home more comfortable.
But, that is really all there is to a 2 stage furnace... now variable speed furnace with modulating gas valves are much the same except there is much more in energy savings from the variable speed blower motor.
Learn more about variable speed here.