Raksha means protection and bandhan means a bond. The thread is a prayer for protection, tied with love; in older tradition it was also tied by priests on the wrists of kings and patrons, and by wives on husbands going to battle. Over time it has become above all a celebration of the bond between brothers and sisters, including cousins and those who choose to be siblings.
The festival is about mutual care rather than one-way duty. Many sisters tie rakhi to each other, brothers tie rakhi to sisters, and people tie rakhi to soldiers, friends, neighbours and even trees, as a promise to look after one another and the world around them.
Shravana Purnima is also sacred for other reasons. In South India it is the day of renewing the sacred thread (Upakarma), on the west coast fishing communities honour the sea, and in parts of eastern India it ends the swing festival of Radha and Krishna.
In one story from the Puranas, the gods were losing a long war against the demons. Indra's wife Shachi (Indrani), on the advice of the teacher Brihaspati, tied a thread empowered with prayers on Indra's wrist on Shravana Purnima, and Indra went on to win. This is the origin of the mantra recited while tying the rakhi. Another story tells of King Bali, who won Vishnu's promise to stay with him as his guard. To bring Vishnu home, Lakshmi tied a thread on Bali's wrist as his sister, and when he offered her a gift, she asked for Vishnu's return.
A popular story from the Mahabharata tells that when Krishna cut his finger, Draupadi tore a strip from her sari and tied it around the wound. Krishna promised to protect her, and kept that promise when she was humiliated in the Kaurava court, by miraculously making her sari endless. The story is often told to show that the rakhi bond is one of love and protection given freely.