It means wakefulness or watchfulness and constitutes a condition of sobriety acquired following a period of catharsis.
St. Hesychios the Priest defines nepsis as "a continual fixing and halting of thought at the entrance to the heart.
ὁ ἀντίδικος ὑμῶν διάβολος ὡς λέων ὠρυόμενος περιπατεῖ ζητῶν τινα καταπιεῖν — NIV: Be alert and of sober mind.
[2] In Orthodox Christianity, the struggle against the corruption of the passions is conducted through ascetic effort to purify the soul (asceticism from Greek: askesis "exercise").
[3] Purification of the soul, which is achieved only through the help of divine grace, is pursued through one's efforts to fulfill the commandments of Christ, participation in the Holy Mysteries of the Christian Orthodox Church, private prayer including devotion to the Jesus Prayer, fasting according to the Church calendar, study of Holy Scripture and the lives of the saints, and vigilant watchfulness over the thoughts to prevent sinful thoughts from becoming sinful actions, and then passions.