When a serious student of Zen (literally "meditation," a form of Buddhism in Japan that emphasizes meditation-- or zazen--over other spiritual practices as a means of achieving enlightenment) is recognized by his or her teacher as having gained a state of enlightenment comparable to the teacher’s own, he or she is given transmission, or permission to carry on the same form of teaching, thus becoming a dharma successor.
This official confirmation, inka, means that the student may now become a teacher on his or her own.
Dharma generally means law or the way of the universe. Specifically the word refers to the teachings of the Buddha.