Sleep is actually more important than food or water.
Scientists reckon that the human body can survive for up to eleven days without food or water, but only five days without sleep - mainly, as suggested, to allow the brain to assimilate information and 're-set' itself for the next period of activity.
I have always believed that biologically, we work on a 48 hour cycle, although culturally, we work on a 24 hour cycle. That's why if you have an early night, you don;t feel that much better the day after, but the day after thatm, your energy levels rise.
I have never ever felt rested or refrehsed, because I suffer from borderline sleep apnoea, which means I rarely, if ever achieve the correct depth of sleep, so if I get up at five a.m., or two p.m., I feel exactly the same.