What causes a clicking sound under the wood floors in your home?

The clicking noises are caused by the duct-work under the floor. When hot or cool air is run through them, the duct-work will either expand or contract with the temperature change, making clicking noises at the joints to adjust for the expansion/contraction. The other possibility is there is a loose floorboard where a nail missed the joist, and the floor creaks when you walk on it.