Heat always moves to colder surfaces.
In the solar home, the free solar energy first heats up the air. Since the mass floors and walls are cooler, the heat is absorbed and conducted into these materials. Later, when the sun has set and the room air temperature falls, it will reach a point where the mass materials are warmer than the room air temperature. Since heat seeks out cold, the stored energy will now return to the room. The more mass in the home, the more energy that can be stored.