Yes, it does. When the outside air is above a certain temperature your building won't need heating. This is what we will call the 'base temperature'; in the UK it's common to assume a value of 15.5 Celsius, but this is just a historical convention. If the average outside air temperature on a given day is below this base temperature, you will need heat; and your heat requirement that day will be in proportion to the temperature deficit in degrees. Add up the daily temperature deficits over a month, and you get cumulative degree-days (degrees multiplied by days, do you see?). And these cumulative degree days are, by definition, proportional to cumulative heat requirements over the same period. Thus a month in which 360 degree-days are clocked up is 'twice as cold' as one with a total of 180 degree-days.
Don't get hung up on how degree days are actually calculated. It is a little more involved than I have implied, but the end result is the important thing: your space-heating demand is proportional to the regional degree-day value for the month in question.
Incidentally, you don't have to wait a month. You can accumulate degree-days over a week, (or any other interval); you can vary the base temperature to match the actual characteristics of a specific building; and if you have a cooling system you can reverse the arithmetic and look for excess temperatures above the base (no-cooling-needed) temperature.
The benefits of this are tremendous: