The term comes from the New Testament 1st epistle Peter (5:8, νήψατε, γρηγορήσατε. ὁ ἀντίδικος ὑμῶν διάβολος ὡς λέων ὠρυόμενος περιπατεῖ ζητῶν τινα καταπιεῖν - NIV: Be alert and of sober mind. Your enemy the devil prowls around like a roaring lion looking for someone to devour.) There nepsis appears in a verb form, in the imperative mood, as an urgent command to vigilance and awakeness: "be alert and awake".
Nepsis is a state of watchfulness or sobriety acquired following a long period of catharsis. Perhaps most associated with Orthodox monasticism, numerable references to nepsis are made in The Philokalia (the full title of The Philokalia being The Philokalia of the Niptic Fathers). Parallels could likely be made between nepsis and Buddhist mindfulness, Islamic dhikr, and Jewish devekut.
Related to Asceticism
In Eastern Christianity, the Christian's struggle against the world of passions, corruptions and illusions is called asceticism (from Greek: ascesis=exercise). This involves "bringing the head into the heart" - long periods of introspection, self-criticism, and vigilance.
Greek monks also used the teachings of Plato in the Republic, interpreting Plato's triune soul (and the process involved in ordering it) as related to the ascetic's struggle.
As the Christian becomes purified, in time he reaches the stage of Theoria or illumination. At this point, the contemplative life begins, and watchfulness takes on another meaning entirely. Ultimately, the goal of the Eastern Christian is called theosis, or the "deification" of man. According to St. Athanasius and others, "God became man so man can become god."