Jesus mythicism is, put simply, the position that Jesus Christ was not a historical figure, but a mythic figure much like King Arthur or Prometheus. Early Christians - including the Gnostics and Marcionites - constructed the Jesus figure out of a variety of sources. Different mythicists point to different parallels: the dying and rising gods Osiris and Adonis, ideas from mystery religions including Mithraism and from Indian ideas about Krishna.
The Jesus mythicist position can be traced back to the nineteenth century with the work of the historian Bruno Bauer and the Dutch radical theological school. More recently, Jesus mythicism has been advocated by scholars including Earl Doherty, Robert M. Price, "Acharya S" and George Albert Wells. In 2005, Jesus mythicism was the subject of a controversial anti-religious film called The God Who Wasn't There.
Needless to say, Jesus mythicism has not been widely accepted by the theological establishment or the historical community, and is considered quite toxic to Christian belief.