What is Neo Advaita?

Answer 1

I've not heard this term before exactly but persons have called what I have followed for the past 25 years "reformed Vedanta." Advaita is usually used as a term that distinguishes nondual Vedanta (Hinduism based on the Vedas Upanishads rather than the Tantras and Agamas) from dualistic Vedanta. Reformed Vedanta was taught by the 19th century Bengali holy man Sri Ramakrishna and his disciples, of whom Swami Vivekananda was the most prominent. The gist is that "God is real, the world is illusory." An accessible scripture to get an idea about Advaita Vedanta is the Crest Jewel of Discrimination (also called the Vivekachudamani) by Shankaracharya (the partriarch of Advaita Vedanta).

Sri Ramana Maharshi is another (more) modern teacher of Advaita Vedanta.

Certain forms of Tantric Hinduism, such as that taught by Nisargadatta Maharaj--my favorite, actually-- also are modern Advaitic.

An example of dualists (dvaita) Vedanta is the Hare Krishna movement.