Hindus have several significant events associated with Diwali festival:
Return of Lord Rama to Ayodhya: Diwali also celebrates the return of Lord Rama, King of Ayodhya, with his wife Sita and brother Lakshmana to Ayodhya after a 14 year exile, and a war in which he killed the demon king Ravana. It is believed that the people of Ayodhya lit oil lamps along the way to light their path in the darkness. Since Lord Rama traveled from South India to his kingdom in North India, he passed through the south earlier. This is the reason why the festival is celebrated a day earlier in South India.
The Killing of Narakasura: Celebrated as Naraka Chaturdasi, two days before Diwali day, it commemorates the killing of Narakasura, an evil demon who created havoc, by Lord Krishna's wife Satyabhama. This happened in the Dwapar Yuga during this time of Lord Krishna's avatar. In another version, the demon was killed by Lord Krishna (Lord krishna provokes his wife Satyabhama to kill Narakasura by pretending to be injured by the demon. Narakasura can only be killed by his mother, Satyabhama) himself. Before Narakasura's death, he requested a boon from his mother, Satyabhama (believed to be an Avatar of Bhudevi - Narakasura' mother), that everyone should celebrate his death with colorful light.
Austerities of Shakti: According to the Skanda Purana, the goddess Shakti observed 21 days of austerity starting from ashtami of shukla paksha (eighth day of the waxing period of moon) to get half of the body of Lord Shiva. This vrata (austerity) is known as kedhara vrata. Deepavali is the completion day of this austerity. This is the day Lord Shiva accepted Shakti into the left half of the form and appeared as Ardhanarishvara. The ardent devotees observe this 21 days vrata by making a kalasha with 21 threads on it and 21 types of offerings for 35 days. The final day is celebrated as kedhara gauri vrata.
Krishna defeating Indra: Govardhan Puja is celebrated the day after Diwali. It is the day Lord Krishna defeated Indra, the deity of thunder and rain. As per the story, Krishna saw huge preparations for the annual offering to Lord Indra and questions his father Nanda about it. He debated with the villagers about what their 'dharma' truly was. They were farmers, they should do their duty and concentrate on farming and protection of their cattle. He continued to say that all human beings should merely do their 'karma', to the best of their ability and not pray for natural phenomenon. The villagers were convinced by Krishna, and did not proceed with the special puja (prayer). Indra was then angered, and flooded the village. Krishna then lifted Mt. Govardhan and held it up as protection to his people and cattle from the rain. Indra finally accepted defeat and recognized Krishna as supreme. This aspect of Krishna's life is mostly glossed over - but it actually set up the basis of the 'karma' philosophy later detailed in the Bhagavat Gita.
Bali's return to the nether world: In Bhavishyottara and Brahma Vaivarta Purana, Diwali is associated with the Daitya king Bali, who is allowed to return to earth once a year. However in Kerala this is the reason 'Onam' is celebrated. 'Onam' festival falls around the month of August-September.