By simply turning on your side, you are reopening the airway and allowing air to travel unhindered, thus eliminating the sound.
If you believe that you or someone you love may be suffering from OSA (the most common, though by no means exclusive or conclusive, symptom of which is severe snoring) a trip to a sleep clinic is highly recommended.
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If you can make a snoring noise with your mouth open and closed, try this: stick your tongue out as far as it will go and grip it between your teeth.