Your ears pop during takeoff and landing because of tiny tubes, full of air, that connect your ears to your throat. Air pressure changes during ascent and descent cause pressure differences within your head, and those tubes become blocked. When you yawn or swallow, you open the tubes and equalize the pressure. Chewing gum helps you generate saliva to swallow, but you don't really need the gum at all!
Credit: Smithsonian Institution, National Air and Space Museum