Dev Diwali festival is celebrated 15 days after Diwali on the day of Kartik Purnima, ie. full moon day of Kartik month according to Vedic astrology. People often associate Kartik Purnima with different gods and legends. Some say it is celebrated to mark the birth anniversary of Lord Kartik, son of Lord Shiva, whereas others are of the opinion it is the day when Lord Vishnu took his very first avatar- Matsya.
The most popular legend is that on this day Lord Shiva destroyed three cities built by three demon princes Taarakaaksha, Kamalaaksha and Vidyunmaali who were sons of the demon king Taraka. This is where Shiva got the name Tripurari orTripuraanti from. As the news of the destruction of three cities reached the gods who were being harassed by the atrocities of demon princes rejoiced and celebrated the day by lighting lamps to please Lord Shiva.
The demon Tripura represent the ego-mind and the three sons represent Satwa (knowledge), Rajas(activity) and Tamas ( dullness) of the who mind. The three cities built by three demons represent the qualities of lust, anger and greed which doesn't allow divine qualities to manifest. Thus one can remain stuck in the world woven by ego-mind (Maya) and its 3 gunas and unless destroyed by spiritual knowledge of Self, which Lord Shiva represents. A spiritual seeker must understand & overcome the ego-mind its nature by constantly transmuting all his energies to attain Self-realisation & see ones Shiva-like auspicious Self in every being.
On Dev Diwali thousands of devotees come together & lit diyas and lamps & take a dip in the holy Ganges (also called 'Kartik snan' ) & worship Lord Shiva. It is believed that taking a dip into Ganga on Dev Diwali during full moon night helps a seeker evolve his or her spiritual consciousness.