Rinpoche is an honorific meaning precious one, addressed to teachers of high standing in Tibetan Buddhism, and it is a form of address rather than an office, conferring nothing of itself.
A title of reverence
The word is attached to the name of a lama held in high regard, above all to recognised reincarnate teachers, the tulkus, and to abbots and masters of eminence, as a mark of the reverence in which they are held, so it functions much as a title of honour rather than as a defined rank with its own powers. To be addressed as rinpoche signals that the person is regarded as a precious teacher, but the honorific does not by itself carry authority, which rests on the actual standing, learning and lineage of the person.
Recognition behind the title
The title most often accompanies recognition as a reincarnate lama, a tulku identified as the rebirth of a previous teacher and enthroned in his line, and it is this recognition, or genuine mastery and lineage, that carries the real authority, the honorific merely marking it. The common Western tendency to treat rinpoche as though it were an office in itself mistakes a term of respect for a rank. The word thus belongs with the other honorifics of the Buddhist world that express reverence for a teacher, and understanding it rightly means seeing that it names the esteem in which a person is held rather than a position that has been conferred upon them.