There lived a Daanav named Tripur in an earlier Sat Yug. He used to kill Devtaa and hid in his city which was in sky. He got Vardaan from Brahmaa Jee that is why he was very powerful, and with the help of that he was trying to destroy three Lok.

Seeing this, Devtaa went to Shankar Jee and told their saga. Shiv Jee immediately picked his Aajagava bow and killed that Daanav seeing him by his Divine sight from quite a distance. That Daanav fell down on Prithvi.

Another Version

Taarakaasur had 3 sons - Taarakaaksh, Kamalaaksh and Vidyunmaalee. They asked Daanav architect Maya Daanav to build 3 cities for them which should be unique in the world. So Maya Daanav built three cities for them - one of gold, another of silver and another of iron. And he built them in the sky. He warned them not to tread in the paths of gods, but they were very arrogant and they started troubling gods. Devtaa took their complaint to Shiv Jee and he, at an appropriate time, shot an arrow which destroyed all the three cities together. Since he destroyed three Asur living in three cities together, he came to be known as Tri-Puraaree.

Since three Asur lived in three cities, that is why those three Asur called Tripur Asur. (read Vidyunmaalee for detailed description of their Var from Brahmaa Jee)

Importance of Kaarttik Poornimaa

1. Tripuraasur was killed on Kaartik Poornimaa, that is why it is called Tripuree Poornimaa also.

2. Guru Naanak was born on this day.

3. Every year a fair is organized on Kaarttik Poornimaa in Pushkar Jee and thousands of people take bath there on this day.

[Padm Puraan, 1/24]
[Also in Skand Puraan, Maaheshwar Khand]