[Greek autos self + skopia observation, from skopein examine, look at]
Viewing or examination of oneself; a hallucination of viewing one's own body.
I experienced an autoscopy once in which I floated out of my sleeping body and looked down upon myself from the top corner of the room. I even watched myself turn in the bed, surprised to physically feel the sensation of turning in my completely immaterial self.
There's nothing particularly unusual about my experience, of course, and I've no doubt at all that it was just a particularly vivid dream. Out-of-body experiences have fascinated humans since time immemorial, and although some still put such experiences down to occult or spiritual phenomena, it's generally accepted in mainstream science that there are rational explanations, such as it being a type of hallucination brought about by such diverse factors as brain injury, sleep disorders or deprivation or some other psychological or neurological reason.
What is particularly bizarre is an apparent condition called a negative autoscopy, or occasionally Maartechen Syndrome. This is a psychological condition in which the sufferer is unable to see their own reflection in mirrors or other reflective surfaces, even though the person's reflection is (of course) normal to everyone else. It is apparently extremely rare, and is described in Jan Dirk Blom's Dictionary of Hallucinations as a type of cognitive hallucination.