According to Jimmy Akins, who is a great one for good solid answers, and from whom I lifted this info, it refers to a 24 hour period.
He talks about it in great detail on this page:
http://www.jimmyakin.org/2005/02/how_many_times_.html
So when the period from local midnight to local midnight is 24 hours, that's a "day". Got it. What happens if the period from local midnight to local midnight is something other than 24 hours?