In the Vedantic tradition, the knowledge of the Self is not something one discovers alone from books. It is received from a teacher who has himself received it — just as the Upanishads instruct the seeker to approach a Guru who is learned and established in Brahman.
Parampara means “one after another”: an uninterrupted chain. The Guru–Shishya Parampara is the line of teachers and disciples through which a teaching, a method of interpretation, and a living example are handed on intact. At Sringeri the chain has an institutional form as well: each Acharya initiates his chosen disciple into Sannyasa, names him successor-designate, trains him personally, and is succeeded by him on the Peetham.
The authority of the Jagadguru therefore does not rest on personal charisma or on election. It rests on this succession — on having received the teaching and the seat from one who received them in turn. That is why devotees salute not only their own teacher but the whole Parampara.