Lalitaa Sahastra Naam is given in Brahmaand Puraan in the chapter where the discussion between Hayagreev and Agastya Muni is given. Hayagreev is the Avataar of Vishnu. He has the head of a horse and is believed to be the storehouse of knowledge; and Agastya Jee is one of the very old Rishi who is one of the Sapt Rishi too. One day Agastya Muni asked Hayagreev to tell him about the 1,000 names of Devee, then Hayagreev taught him this Lalitaa Sahastra Naam Stotra to him.

Shiv, one of the Holy Trinity, married Satee, one of Daksh's 60 daughters. Once Daksh did a Yagya, but since he was not keeping good relations with Shiv so he did not invite him in his Yagya. However Satee went to attend that Yagya and Daksh insulted her husband which she could not tolerate and immolated herself then and there only. As a consequence Daksh was killed but later was given life with the head of a goat. This incident upset Shiv so much that he entered into meditation. However Satee reincarnated as Umaa in Himvaan's house. There also she started doing Tap to get Shiv as her husband. (read this story in - Maanas, 1/3;  Daksh; Skand Puraan; - it comes in Shiv Puraan also)

On the other side there arose a great Asur named Sur Padm (read his story in Skand Puraan, Shiv Rahasya) who had a boon that he should be killed by the son of Shiv and Paarvatee. So Devtaa deputed Manmath (Kaam Dev) to wake Shiv from his meditation. In spite of fear of Shiv, Manmath went to Shiv and as he tried to wake him up, he was burnt by the opening of Shiv's third eye in rage. Manmath's wife Rati got very sad and prayed Shiv to bring her husband life back. So he looked at the ashes and a Bandaasur came to life who made the world impotent and ruled Shonitpur.

Devtaa again got troubled and asked the advice from Naarad Jee who advised them to do a Yagya. As they did the Yagya, from that fire rose Lalitaa Tripur Sundaree. She was very beautiful, having long black hair with Chamapak, Ashok and Punag flowers fragrance; nose studded with shining gems; cheeks more red than Padmaraag (ruby) and white teeth. She was so beautiful that even Shiv himself could not take his eyes off. She was given in marriage to Lord Kaameshwar and she started living in Shree Nagar on the top of Meru Parvat.

Now Shree Nagar had 25 streets around it. They are made of iron, steel, copper, lead, alloy of five metals; silver, gold, white Pushparaag stone and red Padmaraag stone; onyx, diamond, Vaidoorya, Indraneel (topaz), pearl, Marakat (Pannaa), coral (Moongaa), nine gems, and mixture of gems and precious stones. In the eighth street there was the forest of Kadamb. Here lived Shyaamalaa. In the 15th street lived Asht Digpaal. In the 16th street lived Varai (Dandinee) who is her Commander-in-Chief. Shyamalaa also has a house here. In the 17th street lived Yoginee. In the 18th street lived Maa Vishnu. In the 19th street lived Eeshaan and in the 20th street lived Taaraa Devee. In the 21st street lived Vaarunee Devee, and in the 22nd street lived Kurukul who was the in-charge of the fort of pride. In the 23rd street lived Maartand Bhairav, in the 24th street lived Moon and in 25th streetlived Manmath in-charge of the forest of love.

In the center of Shree Nagar lived Maa Padm Van (forest of lotus); and within it there is Chintaamani Grih. In its north-east is Chid Agni Kund and on its both sides of eastern gate are the houses of Mantrinee and Dandinee. On its four gates stand Chaduramnaya gods to guard and watch. And within it is Shree Chakra. In the center of Shree Chakra are many decorations.

Devtaa prayed her to kill Bandaasur. When she started for war, she was accompanied by all Siddhi, Braahmee, Karee, Vaishanavee, Varaahee, Maa Aindree, Chaamundee, Lakshmee, Nitya Devtaa, and Aavaran Devtaa. While the army as commanded by Dandinee, assisted by Mantrinee, Jwaalaa Maalinee protected the army by creating the fire around it. They destroyed a big chunk of Bandaasur's army. Baalaa devee killed the son of Bandaasur; and Mantrinee and Dandinee killed his brothers Vishaang and Vishukra.

When Asur tried to block Devee's army, she created Ganesh with the help of Kaameshwar to remove the blockage. Then Bandaasur created the Asur named Hiranyaaksh, Hiranyakashyap and Raavan. At this Devee created 10 Avataar of Vishnu and destroyed them. She killed his army with Paashupat Astra and killed the Asur with Kaameshwar Astra. Gods then praised her.

She recreated Manmath for the good of the world. This is also called "Rahasya Naam Sahastra" also. As Vishnu Sahastra Naam Stotra contains its Phal Shruti with it and is recited with it, Lalitaa Sahastra Naam does not include Phal Shruti. Its Phal Shruti is the part of Maarkandeya Puraan. It was taught by Maarkandeya Muni to Agastya Muni.

Thus this is a  long Sanskrit poem of Durgaa's 1,000 names of the Divine Mother. Some names in the Sahastra Naam are very significant - Shiv Gyaan Pradaayinee,  Shivpriyaa,  Shivdootee  Shiv-aaraadhyaa,  Shivmoorti,  Shivparaa,  Shivankaree,  Shambhaavee,  Shankaree,  Dakshinaamoorti-swaroopinee,  Sadaashiv-pativrataa,  Govind-roopinee,  Vishnu-maayaa Vilaasinee,  Vighna-naashinee,    Sanhaarinee Rudra Roopaa... In the end there is a name "Shree Shiv Shiv-shakti Aikya" - in this way Lalitaa Parameshwaree personifies the union of Shiv and Shakti too.

This Sahastra Naam is extremely powerful and will transform one's mind and body. It is a potent weapon against all mental, physical or other obstacles in life.

Interesting Things About It
(1) An interesting thing about it is that the Sahastra Naam praises A-Dwait through following names
Ekaakinee,  Bhoom-roopaa,  Nir-Dwait,  Dwait-Varjitaa,  Brahmaatmaa-Aikya Swaroopinee

(2) It has been noted in computer sound recordings, that the music gets converted to wave-table figures and the waves formed angles and figures of graphic images on computer screen. Similarly when the complete texts of Shree Lalitaa Sahastra Naam is repeatedly recited properly, it forms images resembling a Shree Chakra. It is possible that similar powers exist with other Mantra and Yantra.