A single stage furnace has one heat setting. The furnace is either on at full capacity or it is off.
A two stage furnace has two different heat settings; one full capacity and a second lower heat setting. The advantage of a two stage furnace is that it extends the run time which does a better job distributing the air in your home. This helps improve your homes comfort level while reducing drafty areas.
A modulating furnace will heat on a low capacity until a call for high heat is sent to the furnace. Once a high heat call is initiated the furnace will slowly increase the burner level and blower speed over time, until reaching full capacity. The advantages are potentially reduced noise and better efficiency in some models. A modulating furnace should provide the best comfort level.