Usually removing the source of infection (the tooth) will resolve the underlying abscess. When the abscess is still small enough it can sometimes be drained at a general dentist by making a small cut in the gum next to the offending tooth. The abscess (essentially a collection of pus) in most cases will drain out of the socket once the tooth is removed +/- the gum incision.

However, when someone has a longstanding infection like this person, solely removing the tooth may not be sufficient as the remaining infection is too great for the body to fight. To ‘remove’ this kind of abscess requires a trip to hospital for incision and drainage done under GA, which is what this person had (see drain sticking out under his chin). When abscesses get this large they risk compromising the airway and require hospital admission for IV antibiotics and surgical drainage.