The Grace Made Edible
Prasādam (Sanskrit: prasāda = grace, clarity, favour) is the consecrated food — or any consecrated object — that has been received by Bhagavān during worship (naivedyam) and is then distributed to devotees. In the Śrī Vaiṣṇava tradition, prasādam is not merely 'food that was offered' but the actual remnants of what Bhagavān has accepted and blessed — śeṣam ('the remainder/that which was left by the Master').
Śeṣam
The Tamil/Sanskrit pair prasādam-śeṣam expresses the same reality from two angles: prasādam from the giving side (Bhagavān's grace expressed as food), śeṣam from the receiving side (we are His servants eating what He has left). Receiving prasādam purifies the devotee — it is a direct transmission of Bhagavān's grace into the body.
Extension to Āzhvārs and Ācāryas
In the sampradāya, prasādam extends beyond food offered to the temple deity. The remnants of food eaten by a revered Āzhvār, Ācārya, or bhāgavata (devotee) are equally considered prasādam — tadīya śeṣam. Receiving such prasādam is considered highly auspicious.