Sampradāya (from sam- = completely/properly + pra-dā = to give/transmit) means 'that which is thoroughly handed down' — the living, continuous tradition of a religious or philosophical community. In the Śrī Vaiṣṇava context, sampradāya is not merely a body of texts or doctrines but a living relationship of initiation, teaching, and grace that flows from Bhagavān Himself through an unbroken chain of Āchāryas. The correct designation is Śrī-Vaiṣṇava-sampradāya, also called the Ubhaya-Vedānta-sampradāya (the tradition of both Sanskrit Vedas and Tamil Divya Prabandham) or the Viśiṣṭādvaita-sampradāya (from its philosophical standpoint).
The paramparā (lineage) is narrated in the Taniyans (invocatory verses) prefixed to the Divya Prabandham and in hagiographic works such as the Guruparamparā Prabhāvam and Periya Tirumuṭi Aṭaivu. It begins with Bhagavān Nārāyaṇa Himself, who first transmitted the knowledge to Śrī Mahālakṣmī (Periya Pirāṭṭiyār); thence to Viṣvaksena (the commander of Bhagavān's celestial hosts, who serves as the primordial disciple); thence to Nammāzhvār (Śaṭhakopa), who received this knowledge by Bhagavān's special grace and deposited it in the Tiruvāymozhi; thence to Nāthamunigaḷ, who recovered the Nālāyira Divya Prabandham from obscurity; and through Uyyakkoṇḍār, Maṇakkāl Nambi, Āḷavandār (Yāmunācārya), to the supreme systematiser Śrī Rāmānujācārya, who gave the tradition its definitive philosophical and institutional form.
After Rāmānuja, the sampradāya branched into the Vaḍakalai (Northern/Sanskrit-emphasis) and Teṉkalai (Southern/Tamil-emphasis) sub-traditions, each with its own lineage of Āchāryas, commentarial schools, and liturgical practices. Both sub-traditions acknowledge the same paramparā up to and including Rāmānuja; divergences relate chiefly to the role of prapatti theology, the status of Āndāḷ, and certain ritual details. In both, the sampradāya is understood to be alive only so long as the unbroken transmission from Āchārya to disciple continues — a tradition without a living Āchārya lineage is considered a luptam (lapsed) tradition, not a true sampradāya.