What does double occupancy mean in a hotel rate?

Single occupancy = one person
Double occupancy = two people

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A hotel room that is $100 per night, based on double occupancy, means the room is $100 per night whether one or two people stay there. Three people staying there would cost more than $100 per night.

"Per person based on double occupancy" means that the room rate is charged for each person who stays there, and they expect that two people will stay there.