Significance
Diwali, the festival of lights, is a five day long celebration. The fifth or the last day of Diwali is Bhaiya Dooj, popularly known as Bhai Dooj. Bhai Dooj falls on the second day after the new moon. And it is a day to pray for the long life of one's brother, who is referred to as “bhayya or bhai”.
This festival marks the love between sisters and brothers, and is celebrated to strengthen the bond of care and affection between the two. Through the means of this festival, sisters commemorate their brothers with an auspicious tilak or a vermilion mark on their foreheads. In return, brothers give gifts to their sisters.
History
Once upon a time, long long ago, Surya, the sun God, was married to a beautiful princess called Samjna (also pronounced as Sangya). In the course of a year, she presented him with twins. The twins were christened Yama, and Varni or Yamuna, and they grew up together. However, Samjna, after some time, was unable to bear the brilliance of her husband, and so decided to go back to earth. However, she left her shadow, Chaya, her exact replica, behind, so that to Surya, it would appear that she was still there.
Chaya turned out to be a cruel stepmother and was very unkind to the twins. She soon gave birth to her own children, and then convinced Surya to drive out Samjna’s twins, Yama and Varni from the heavens. Varni fell to earth and became the river Yamuna, and Yama went to the underworld (hell) and became the Lord of Death.
Many years passed since this incident. Varni married a handsome prince and was content and happy in her life. But she missed her brother and yearned to see him. Yama, too, missed his sister and decided one day to visit her. Overjoyed by news of her brother's visit, Varni prepared a great feast in his honor. It was two days into Deepavali, so her home was already decorated with lamps. She lovingly prepared a feast, including all the sweets and delicacies that her brother loved. Her husband, the handsome prince, was very happy seeing Varni so dedicatedly preparing a welcome for her brother.
Yama, too, was delighted by his sister's loving welcome, and the brother and sister spent a pleasant evening in each other's company, after their long period of separation. When it was time for Yama to leave, he turned to his sister and said, "Dear Varni, you have welcomed me so lovingly. But I did not bring you a gift. Ask, therefore, for something and it will be yours."
"Your visit is gift enough," replied Varni lovingly. "I have no need for anything else."
But Yama was persistent. "You must let me give you a gift," he insisted.
"Okay," agreed Varni, taking a moment to think. "I ask that all brothers should remember their sisters on this day and visit them if they can, and that, on this day, all sisters should pray for the happiness of their brothers."
"So be it!" proclaimed Yama, "And I grant all brothers who give their sisters a loving gift on this day a long and healthy life!"
Determination of Date:
Bhaiya Dooj is celebrated on Kartik Krishna Dwitiya falling at Aprahan. If Kartik Krishna Dwitiya falls on two days and falls or does not fall during Aprahan then it is celebrated on second day otherwise on first day.
How to Celebrate
So traditionally, all brothers visit their sisters on this day and give them gifts. Sisters too, pray for their brothers' long life and good health, and general well-being.