The very common and generally accepted view is because we burns Deep (lamps) and some extra lighting. Diwali is significantly comes at the end of Aaso month (last month according to Indian calendar) which means at the end of year, which also means beginning of New Year. So it is like day set and sun rise, similarly year ends and we welcome New Year with lights.
According to Hinduism, Shree Ram came along with Sita and Laxman after 14 years of Vanvas and Ayodhya along with whole country got their real king back, i.e. like a real light of Country came back. According to Jainism, It is a day of Nirvana of Lord Mahaveer. So lord Mahaveer considered as light of Yug and after his Nirvan, there was darkness got splash on earth. To remove that darkness, people brighten up lamps and celebrated next day as new beginning.
Other view can be like, India is farming country and Diwali is showing end of Rainy season and start of winter, which means whatever efforts farmers have made during monsoon, now the time have arrived to get return of that.
