The didgeridoo treats sleep apnea by exercising the muscles in the back of the throat.
Sleep specialists and even the famous TV doctor, Dr. Oz, recommend patients to use a didgeridoo to treat their symptoms if they find CPAP treatments uncomfortable and problematic. According to Dr. Oz, the didgeridoo can help to "exercise the muscles in the back of the throat that cause snoring while you sleep. Those muscles get lax while you sleep so, by exercising them with the didgeridoo [...] you strengthen the muscles so they don't collapse while you sleep."
Photo source: Dr. Oz and the didgeridoo/ABC News