Firstly, welcome!
Pockets are the small gap between your teeth and your gum which, generally due to infection is bigger/deeper than it should be. Sometimes when the gums are infected this gap gets much bigger. If allowed to continue without treating the infection, debris and bacteria continue to multiply and the gum can recede back from where it should be on the teeth and make you look 'long in the tooth. The dentine can get exposed and teeth become more sensitive to hot/cold and sometimes sweet.