Advaita by default has come to mean the doctrine of Shankara (8th Century CE). It was primarily for Mumukshu's - people with a keen desire to be liberated and were willing to give up everything for it. Obviously, this was reserved for learned Brahmins, who would then become Sanyasins, approach a qualified Guru (who would test the student too before taking him on) and learn from him. Advaita endorsed the idea of Jivan-mukti or liberation, while the body is still alive. It was a different time. Books were not printed and there were no book stores or public libraries. Literature, in the form of manuscripts, was in the hands of teachers or Royal libraries and was only available to students and scholars.
Fast forward to the 19th Century. All literature, which was previously only available as manuscripts, were now available as printed books. Anyone could read anything, without restriction, without prerequisites and more importantly, without a personal Guru. Advaita became popular in the West, due to Vivekananda and then later, Ramana. But there was a difference. Without the rigor and the discipline of the Guru-Shishya relationship, people read into the doctrine what they wished. Anything and everything passed as Advaita so long as a couple of basic points were honored (all is one, I am God, everything is God).
Neo-Advaita is the label that covers all these new, tangential beliefs, which consider themselves Advaita, but were not endorsed by Shankara or by any of the present traditional Advaita scholars. Such labeling is not new. During the 12th Century CE, Gangesha created "Navya Nyaya" or neo-Nyaya as the more traditional Nyaya was dying out and this was his attempt to bring it back in a form that was more relevant to his time.
Is it a bad thing? Not necessarily. It is the nature of religion that it evolves and adapts to times. The neo-Advaita label serves to keep the distinction between traditional Advaita (which is still alive and well) and the newer beliefs and methods that pass off as Advaita.
