In the most simplistic terms, an air filter is a device which removes contaminants from the air.
The simple truth is that the air in your house is dirty, very dirty. The average house contains a wide variety of contaminants. The closed nature of a house means these contaminants concentrate, leading to an atmosphere which is potentially 100 times more polluted than the outside air.
As the renowned Dr. Laura Schlessinger once said, “If you do not have an air purifier, you ARE the air purifier.” This rings true as often the only thing that filters the air in a home is the human lungs.