Sound bizarre? It's based on Politzerization (also called the Politzer maneuver), which works by blowing air up the nose during swallowing. As the person doing it swallows, the air blown up their nose is diverted to the Eustachian tubes, inflating them and equalizing pressure in the sinuses.
When my sinusitis flares up so badly my Eustachian tubes close, I usually fix it by exhaling with my mouth closed and nose pinched shut, known as a Vasalva maneuver. It works well, but the Politzer maneuver is safer since it's possible to rupture the eardrum by performing a Vasalva maneuver too forcefully.