Bhagavat-prasādham (from Sanskrit prasāda, 'clarity/grace/favour') refers to any food, flower, garland, or ritual substance that has been offered to Bhagavān in worship and is then distributed to devotees. The theological basis is transformative: the object presented to Bhagavān is permeated by His glance and acceptance, so that what returns to the devotee is no longer merely food or a garland but a substance charged with divine grace. Accepting prasādham with the head, the palm, and eventually the mouth is thus a complete act of surrender — one takes into oneself the Lord's own remnant (ucchiṣṭa), which in any other context might imply subordination, but which here is the highest honour.
In Śrī Vaiṣṇava theology, the logic of prasādham rests on the concept of śeṣa-śeṣī: the jīva as śeṣa exists for the pleasure and service of Bhagavān as śeṣī. The devotee's body is itself the Lord's instrument, so consuming His prasādham is a recognition and enactment of this relationship. Nammāzhvār in the Tiruvāymoḷi repeatedly uses the image of the Lord's remnant (ucchal) as the ultimate food, and Āchāryas such as Vedānta Deśika wrote devotional works in which accepting prasādham is equated with the joy of service.
The concept extends naturally to the Āchārya: his nirmalya — the wilted flower garlands, the sandal paste, the tīrtham from his hands — are all treated as prasādham from the Āchārya's person, which itself is a temple of Bhagavān. In many Śrī Vaiṣṇava households, a designated tray preserves the Āchārya's nirmalya received at initiation (Pañca-saṃskāra) or special visits. The everyday act of temple prasādham distribution (usually a small quantity of sweet rice or fruit) is thus the popular expression of a deep theological commitment to the jīva's dependence on and nourishment by divine grace.