A conventional gas furnace works by bringing in the cold air, taking it through a filtration system (hopefully using a good air filter that removes allergens like pollen, dust, bacteria, viruses, and smoke), heating it with a gas burner using a heat exchanger, and distributing the warmed air through your homes duct work.
As the air in your home cools, it returns to the furnace through return air grills and duct work. This air cycles back through the system, going through the air filter, getting heated, and then cycles back through to each room in your home.
A blocked and dirty air filter will keep the air from traveling through your system properly and will result in higher energy bills with less heat, as well as causing your system to break down. It is important to follow the schedule recommended for your system in replacing or cleaning your air filter.