It has started from vedic period ......... there are many stories about Raksha Bandhan ........... 1st. is .....The demon king Mahabali was a great devotee of lord Vishnu. Because of his immense devotion, Vishnu has taken the task of protecting bali's Kingdom leaving his normal place in Vikundam. Goddess lakshmi - the wife of lord Vishnu - has became sad because of this as she wanted lord Vishnu along with her. So she went to Bali and discussed as a Brahmin woman and taken refuge in his palace. On Shravana purnima, she tied Rakhi on King Bali's wrist. Goddess Lakshmi revealed who she is and why she is there. The king was touched by Her and Lord Vishnu's good will and affection towards him and his family, Bali requested Lord Vishnu to accompany her to vaikuntam. Due to this festival is also called Baleva as Bali Raja's devotion to the Lord vishnu. It is said that since that day it has become a tradition to invite sisters on sravan pournima to tie sacred thread of Rakhi or Raksha bandan. ...more

Http://thatshindi.oneindia.in/astrology/2011/astrology-raksha-ban dhan-special-aid0191.html

Please read the story given on the above site.
When thee was a battle between Sur and Asur, Indra was about to be defeated; he approached the Guru Brihaspati. The Indrani wife of Indra then tied a silk thread around the wrist of Indria. The beginning of the festival was by a wife for the welfare of her husband.