The following text is borrowed from today’s Times of India:
Legend has it that when Krishna was injured with a cut on his hand, Draupadi, the Pandavas’ wife, dressed his wound by wrapping a strip of her sari around it. Krishna, touched by her concern for his well-being, swore to repay the debt by protecting her.
Over the years, the spirit of rakhi spread with other stories further emphasizing the importance of the bond. By tying a rakhi, a sister promises to pray for her brother’s well-being and he, in return, promises to protect her.
More stories from the legends, regarding Rakhi can be found in this site.
Picture of Rakhi (above) saved from the Internet.