Naraka means the hellish state of suffering. The day is understood as cleansing away whatever keeps a person in that state: laziness, impurity, anger and ill will. The early oil bath is a physical expression of this, and in much of South India it is the most important moment of the whole Deepavali festival.
The day also has a quiet side. Many families offer water to Yama after the bath and light lamps in the evening for the protection of the household and in memory of ancestors. In eastern India the evening is especially devoted to ancestors.
Culturally, Narak Chaturdashi is the day when the Diwali mood truly begins: new clothes are worn, sweets are shared, the first rows of lamps are lit and children enjoy the first firecrackers.
Narakasura, a powerful demon king of Pragjyotisha, gained great strength and used it to oppress the three worlds. He seized the earrings of Aditi (mother of the gods) and held thousands of women captive. Krishna, accompanied by his wife Satyabhama, went to battle against him. After a fierce fight, Narakasura was defeated, and in many tellings it is Satyabhama who strikes the final blow.
As he was dying, Narakasura asked that the day of his death be remembered with lights and celebration rather than mourning. Krishna returned at dawn and took an oil bath to cleanse himself after the battle, which is why people bathe with oil before sunrise on this day. The freed women were given honour and shelter, and the day became a celebration of release from oppression.