Good question! An ascended master is said to be an adept (who is a person skilled in the use of magic and occult powers) or a holy man/woman who is believed to be teaching the world from another plane of existence. These teachings are performed by means of dreams, visions, or direct voice messages.
Teachings about ascended masters originated with Helena P. Blavatsky (1831-1891), one of the founders of the occult-based Theosophical Society; however, the definition was eventually expanded to include any individual who lived through various incarnations on Earth and fulfilled their divine plan to become "God-like". Once achieved, they are capable of returning to Earth to continue their teachings.
Jesus is considered to be an ascended master, as is John the Baptist who apparently became an Ascended Master "in his life as Elijah, the prophet." Others include Osiris, Egyptian god of the afterlife; Krishna, who is known as a "Cosmic Master"; Swami Vivekananda, an Indian Hindu monk; Brahma; Confucious; Moses (known as Lord Ling in a later life); the Blessed Mother, and a long list of others.
You'll note that a belief in ascended masters presupposes a belief in reincarnation; otherwise, the whole theory behind ascended masters falls apart.
Obviously, there is no such thing as an ascended master and the only evidence we have of their existence comes from mythology, New Age enthusiasts and theosophists.