Think about it as Degree x Days the way we measure a crew's work in man x hours...
It doesn't mean anything in the natural world. It's just an arbitrary way to standardize the count of how much heating you should have done during a day (or month, season, etc.)
Assumes a couple things: first that 65° is the temperature you'd keep your thermostat at and that (Low + High)/2 correctly represents the average temperature.