There are three ways that heat is transferred: Conduction, convection, and radiation. Heat transfers to the air in contact with the heater mainly by conduction, which is a transfer of heat between two objects in physical contact. Heat has a tendency to spread uniformly throughout a substance because its transferred from faster moving to slower moving particles of a fluid when they collide, and its transferred throughout a solid as the particles vibrate.
The heat is then transferred to the air in front of the heater and spread throughout the room mainly by convection. This is when warm air rises because it's less dense and cooler air sinks, creating currents of air called convection currents.
The third type of heat transfer is radiation, which is energy traveling through space. Infra-red heaters transfer heat in this way.