Diwali is a festival of light and no where in Hindu Scriptures is mentioned of cracker usage. But today for many people Diwali celebration is unimaginable without firecrackers.
But there are people who relate the play with firecrackers to the killing of demon Narakasura by Lord Krishna and Satyabhama. The firecrackers are regarded as the effigies of Narakasura who was killed on the day. Thus firecrackers symbolize the victory of the good over evil and restoration of Dharma.
A couple of years ago while explaining the significance of firecrackers during Diwali, Sri Sri Ravi Shankar said – Watching the firecrackers gives a relief to the explosive tendencies inside. When the explosion happens outside, the explosion inside is diffused.