A swami is one who has taken sannyasa, formal renunciation, and the renunciation is understood to leave behind caste, family, ritual obligation and property together.
Renunciation as a passage out
The word means one who is master of himself, and the swami has passed through the rite of renunciation by which a person abandons the settled duties of the householder, the obligations of caste, the ties of family, and the ownership of property, entering the fourth and final stage of life as a wandering or monastic renunciant devoted to liberation. In the classical understanding the renunciant is held to have died to his former social self, and the rite includes performing his own funeral rites, so that he is reborn beyond the order of caste and duty.
Entry and order
The title is taken on initiation into sannyasa, often within one of the organised monastic orders that trace themselves to the great teachers, such as the ten-named order attributed to Shankara, and the new renunciant receives a monastic name and the mark of his order. Not every swami belongs to a formal order, and the term is used broadly for Hindu monks and religious teachers. The office has close counterparts in the Jain and Buddhist renunciant, all sharing the pattern of a formal leaving of ordinary life for a spiritual end, but the swami renunciation carries the particular sense of stepping outside the caste order that structures Hindu society.