Quick rundown for those not in the know.
Clay is a synthetic polymer which is very smooth and sticky. As we drive the metallic brake dust that gets all over our wheels also gets all over the road. This brake dust is kicked up by cars in front of us and as hot micro razor blades is lodged into the clear coat (top layer of paint) of our cars. This is why when you wash the car and then wax it the wax pad is dirty even though you think the car is clean. The only way to remove these particles is to pull them out. In past years people used paint cleaners which was hard work. Today we use a clay bar. If left untreated these brake dust and atmospheric fallout can oxidize (rust) and this is why you see little orange dots on the car, especially visible on white paint. These rusted particles act to lift the clear coat and eventually cause dull and peeling paint. We need to remove them and seal the paint with a good wax.
Often when these particles are removed we are left with uneven surfaces in the clear coat. They can be permanently fixed with a polish which acts to remove and even out the surface or with a glaze which simply temporarily fills the void. Below is a half ass attempt at illustrating this. Take the zip lock test. Wash your car and then place your hand inside a zip lock bag and run it across your hood. If you feel it's grainy you need to clay. Paint surface should feel like silk.