What really happens when a body is tired?
Its still not clear why we need to sleep (as distinguished from the question of why our body gets fatigued in physical exertion).  A popular idea is that the brain needs to 'catch up' and reorganize itself given all the stimulus it has had from the previous day.  This 2010 National Geographic article says it all:


  I asked William Dement, the retired dean of sleep studies, a co-discoverer of REM sleep, and co-founder of the Stanford Sleep Medicine Center, to tell me what he knew, after 50 years of research, about the reason we sleep. “As far as I know,” he answered, “the only reason we need to sleep that is really, really solid is because we get sleepy.”


It is clear that we need sleep and that we become less reliable at tasks when we are sleep deprived.  eventually we become completely unable to function.  

I'm not sure anyone can answer the last question - why does conscious effort help us to perform tasks?  one would have to understand/define the neurology of consciousness to answer that question.  That is still a bigger question that remains open I think.