The katha of Yama and Yamuna
Sanjna, wife of Surya Dev, had two children — a son, Yamraj, and a daughter, Yamuna. Yamuna loved her brother very much and kept inviting him home for a meal.
Yamraj was the god of death and so busy with his work that he could never go to his sister's home. One day, on Kartik Shukla Dwitiya, Yamuna invited him again with great love. Yamraj thought, 'I am the one who takes everyone's life; no one invites me to their home. My sister invites me with so much love — I will surely go.'
When Yamraj reached his sister's home, Yamuna's joy knew no bounds. She bathed, put a tilak on her brother, did his aarti and fed him many dishes.
Pleased, Yamraj said, 'Sister, ask for a boon.' Yamuna said, 'Brother, come to my home on this day every year, and may any brother who goes to his sister's home on this day and receives tilak have no fear of you.' Yamraj said 'Tathastu' (so be it).
Since then this day is called Yam Dwitiya or Bhai Dooj. It is believed that if brother and sister bathe in the Yamuna together on this day, they earn great merit.
This is OmKiran Bhakti's retelling of the traditional katha in simple English; details of the katha vary slightly from region to region.