Sexual self-restraint or chastity.
1. Since the prayer or sacred word (brahman) came to be identified with the Vedic hymns, a brahmachari was regared as a student of the Veda as well as a disciple of Brahman.
In later Hinduism this remnant of early Brahmanism was preserved as the first prescribed stage (ashrama) of Aryan life, characterized by studentship under a competent teacher (guru) and adherence to a vow of celibacy. The stage itself is called brahmacharya."
(Sources of Indian Tradition, de Bary, 16)
2. It is one of Patanjali's five yamas. The goal is the complete elimination of sexual desire.