Origin story
When Mahabali's rule became too proud, Vishnu took birth as the dwarf Vamana and asked for three paces of land. With two steps he covered earth and heaven, and with the third he pressed Mahabali into Patala, granting him the boon of returning to Kerala each year at Onam.
The umbrella, the kamandalu and the dwarf form express humility and the vastness hidden in the small. The three steps are the three worlds and the three Vedas, and the story is the ritual heart of Onam, when Kerala remembers the king who loved his people.
Source: Wikipedia: Vamana — https://en.wikipedia.org/wiki/Vamana
Symbolism
The umbrella, the kamandalu and the dwarf form express humility and the vastness hidden in the small. The three steps are the three worlds and the three Vedas.
Sloka
1
Shantakaram Bhujagashayanam
शान्ताकारं भुजगशयनं पद्मनाभं सुरेशं विश्वाधारं गगनसदृशं मेघवर्णं शुभाङ्गम्। लक्ष्मीकान्तं कमलनयनं योगिभिर्ध्यानगम्यं वन्दे विष्णुं भवभयहरं सर्वलोकैकनाथम्॥
Śāntākāraṃ Bhujagaśayanaṃ Padmanābhaṃ Sureśaṃ Viśvādhāraṃ Gaganasadṛśaṃ Meghavarṇaṃ Śubhāṅgam, Lakṣmīkāntaṃ Kamalanayanaṃ Yogibhir Dhyānagamyaṃ Vande Viṣṇuṃ Bhavabhayaharaṃ Sarvalokaikanātham
Meaning — I bow to Vishnu, serene and reclining on the serpent, the lord of the gods, the support of the universe, sky-like and cloud-hued, beloved of Lakshmi, lotus-eyed, reached by yogis in meditation, the remover of the fear of existence and the sole lord of all worlds.
Recited for: Dhyana before Vishnu and Vamana worship
