Neoplatonism (also Neo-Platonism) is the modern term for a school of religious and mystical philosophy that took shape in the 3rd century AD, founded by Plotinus and based on the teachings of Plato and earlier Platonists.
The term - neuplatonisch - was first coined by a German historian. The early Neoplatonists, however, like Plotinus and Porphyry would probably have considered themselves simply "Platonists", and the modern distinction is due to the perception that their philosophy contained enough unique interpretations of Plato to make it substantively different from what Plato wrote and believed.
Later movements of Neoplatonism, such as those of Iamblichus and Proclus, kept to these principles whilst adding mechanisms by which the spiritual world could be viewed directly – thus they share the aims of the Sufis, Quakers, Shakers, Gnostics and Zen Buddhists in wanting to understand something of the spiritual world using direct experience. We could thus call them the ‘mystic branch’ of Platonism.
It is worth mentionning that Neoplatonism strongly influenced Christian thinkers (such as Augustine, Boethius, Pseudo-Dionysius, John Scotus Eriugena, and Bonaventura). Neoplatonism also influenced medieval Islamic and Jewish thinkers such as al-Farabi and Maimonides.
The Enneads of Plotinus are the primary and classical document of Neoplatonism. As a form of mysticism, it contains theoretical and practical parts, the first dealing with the high origin of the human soul, and the second showing the way by which the soul may again return to the Eternal and Supreme. The system can be divided between the invisible world and the phenomenal world. The invisible world being the spiritual/software world; the phenomenal world being the hardware world.