This stotra (hymn which praises) occurs in Brahmanda purana (Old epic of the universe) in the Chapter on discussion between Hayagreeva and Agasthya. Hayagreeva is an incamation of Vishnu with the horse head and is believed to be the storehouse of knowledge. Agasthya is one of the great sages of yore who is one of the stars of the constellation great bear. At his request Hayagreeva taught him the most holy 1000 names of Lalitha.
Sree Lalitha Sahasranamam is a very powerful prayer that can be chanted by anyone and it is especially auspicious to chant this on Fridays. Regular chanting with devotion and bhakthi will ward off all evils and you will be blessed with a long and happy life.