The resting brain is actually pretty busy, with nerve cells firing nearly as often as they do in a waking state. One common explanation for this activity holds that during sleep neural circuits replay important memories, a process that strengthens the connections among cells in those circuits, thereby aiding learning.
In the August 2013 Scientific American University of Wisconsin–Madison researchers Giulio Tononi and Chiara Cirelli propose quite a different theory of what happens in the sleeping brain. They suggest that brain activity during slumber must weaken neural connections, not strengthen them, because strengthening would saturate the brain's circuitry and consume so much energy that the brain could not continue to encode new information.
In short, the authors propose that sleep is essential for synaptic homeostasis, a restoring of brain cells to a baseline state. They argue that this function is essential for all creatures and explains the ubiquitous need for sleep. Results of their experiments, conducted over two decades, so far confirm this hypothesis.
In this video of a talk presented at an Allen Institute for Brain Science symposium, Tononi presents this evidence and explains that sleep is the price we pay for the brain's ability to remodel itself in response to the events of waking life.