Headaches due to pressure gradients

I picked up my friend from Germany at the airport today and he told me that he was suffering from a big headache due to the flight.  I explained to him that the reason behind this is because of the changes in pressure when you're flying.  Behind our eardrums, there is an air space.  If the pressure outside of the ear isn't the same as inside of it, the eardrum bends inward or outward, causing your head to hurt.