Whew! I need a Day Off!Most people who say this are referign to needing a day off of work to get some R & R (rest & relaxation). When someone on a true polyphasic sleep schedule, such as Uberman or Dymaxion says this, then they usually mean that they need a day off from life completely: to sleep. A "day off" is a period of sleep time, often 2-5 normal wake periods, which adds up to a decent amount of a whole day. A polyphasic sleeper sleeps this extra time to catch up on their sleep, or rather the phases of sleep they do not normally receive. Some people take this "day off" for only a normal night time period. Two or three normal wake periods might only be 8-12 hours of time. So, it might mean that they simply go to bed one night, possibly early, and then get up when normal monophasic people do in the morning.
There is not a whole lot of historical evidence for this, but some people believe that some or all of the historical figures who lived off true polyphasic sleep would take this "day off" every once in a while: every month or two. When taking a "day off" people often sleep as much as they can. When one has really adapted to poyphasic sleep (not as much if the schedule has a long core sleep period), then he or she will almost always naturally wake up at the end of the nap time, however long that is for their schedule. But, if that person tries to go back to sleep right upon waking, then he will often be able to do so and be able to sleep for a while, as in hours or even much of a whole day.
So, I know what you're thinking. Uh, isn't the point of polyphasic sleep to have less time asleep. So, why would anyone want to sleep for a whole day? Good question. The answer is essentially fear: the fear that those other phases of sleep do serve a purpose. Here's the logic: whether you believe that humans have evolved or were designed, our sleep pattern is no doubt for a reason. If we evolved, then it seems unlikely to believe that no one in our history has tried a different sleeping pattern to gain an advantage. If we were designed, then our sleeping pattern again was likely designed for a reason. So, there is a natural fear that the other sleep phases that are missed in polyphasic sleep are indeed important. See what sleep "experts" say to get some "proof" that a polyphasic sleeper might want to consider catching up on those other phases.