You probably know that hot air rises, and cold air falls. What you don't see is the invisible line that divides the warmer, less dense air from the colder, more dense air. This separation of warm and cold air is called stratification.
Most furnaces are one-stage in operation. This means that they have one large firing rate to heat the home, regardless of the outside temperature. When the temperature outside is 30 below, these furnaces heat your home comfortably because the furnace has to work long and hard to get the job done.
Under these circumstances, there's little stratification because the burner and fan are always running. But when it's warmer outside, the furnace doesn't need to work as hard. When the burner and fan shut off hot air rises, cold air falls, and you feel uncomfortable. You react by turning up the thermostat to compensate for the cold air you're feeling, increasing your energy costs.
With a two-stage furnace, you use a lower firing rate over a longer period of time when outside temperatures are warmer, creating a more uniform temperature throughout the room and making your home more comfortable. In many cases, you're able to set your thermostat lower, thus saving you energy.
With a modulating gas furnace, the firing rate automatically adjusts to the heat loss of your home given the outdoor conditions. This improves comfort and efficiency by further minimizing stratification.