There are three popular stories associated with Raksha Bandhan. The most popular is the one associated with Vishnu’s Vaman Avatar and King Bali. Another story is mentioned in Bhavishya Purana and another in the Mahabharata. The most popular belief is that Raksha Bandhan ritual started after Goddess Lakshmi made King Bali her brother by tying Rakhi.
Vishnu took Vamana Avatar to help Indra, the king of Devas, who was on the verge of being overthrown by King Bali. The Asura King Bali was going to complete 100 yajnas which would automatically grant him the powers of Indra.
Vishnu promised to help Indra. Vishnu appeared as dwarf Vamana and requested for three portions of land that his feet can measure.
King Bali immediately agreed. Vishnu then took giant form and in two steps measured earth and heaven. As there was no place to keep the third step, King Bali asked Vamana to keep the third feet on his head.
King Bali was thus pushed to the netherworld.
Vishnu was moved by the Bhakti and Dharma of King Bali and offered him a boon. King Bali asked Vishnu to reside with him in netherworld.
Vishnu agreed and this caused havoc in the world as there was no Vishnu in Vaikunta to preserve the universe.
Goddess Lakshmi then went to the netherworld and made King Bali her brother. She tied the Rakhi and in return King Bali offered her a boon. As boon she said she wanted to return to Vaikunta with her husband Vishnu. King Bali agreed.
This happened on a Shravan Purnima day and Raksha Bandhan is observed from that day.
Story of Raksha Bandhan In the Mahabharata
In Mahabharata it is stated that when Sri Krishna took the Sudarshana Chakra to kill Shishupala, a small cut happened on his finger. Draupadi who witnessed this immediately tore her dress and tied the cut to stop it from bleeding. Pleased with this act, Sri Krishna promised to protect her. This happened on a Shravan Purnima day. Sri Krishna protected her by providing dress of immeasurable length to Draupadi during the infamous episode in the Hastinapura palace.
Story of Raksha Bandhan in Bhavishya Purana
A story mentioned in the Bhavishya Purana states that Indra was unable to defeat Asuras for 12 long years. Finally, Guru of Devas asked Indra to tie a Raksha using the mantra that was chanted by Goddess Lakshmi while tying Rakhi on King Bali. After chanting the mantra, the Rakhi was tied on Indra’s hand. After this the king of Devas defeated Asuras. The same mantra is chanted even today while tying the Rakhi thread on Raksha Bandhan day.