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 incarnation 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 .
You can find a free copy of Lalita Sahastranam on sanskrit.safire.com . You may also click on the following links to directly download a copy of the stotra in pdf format, which you can easily read on your laptop, mobile, tablet, etc.
www.celextel.org provides english translations of various vedic and religious texts. You may find the english translation of the sahastranam and its glory (i.e. benefits of reciting) from the below mentioned links:
The phalashruti clearly mentions that there has never been and never will be a sacred text which can ever equal the stature of Lalita Sahasranam. Its an apex text on the glory of Maa Lalita.
In my opinion this text is not meant just for Shakti Sadhaks, instead it can be read and practiced by any spiritual seeker. The stotras on Maa Lalita transcends all religions and gender and pave a way towards realisation of all material and spiritual benefits to its devotee. The seeker attains all wished for material comforts and gradually develops dispassion and faith in non-dual self which ultimately leads to self-realisation and liberation from the cycle of birth and death. All this becomes possible only due to the grace of Maa Lalita Tripursundari.
Maa does not require its children to worship her in exchange of her love, as then it would be like trying to overflow an ocean by adding a cup of water to it. She extends her love out of her own nature. Her love and blessings arise out of her unconditional love for her children. The aforesaid being true, still the sages have proclaimed that nothing in this world can be acquired other than by means of self-effort. A seeker must endeavor very hard to get rid of all impurities of mind and dedicate himself in the service of the Lord by means of mind, speech and action.
A sadhak must worship Devi with true devotion and dedication and try to appease Divine Mother. This would help him get rid of all impurities and difficulties of life and enlighten his path towards self-realisation.
As it is said, God is not outside, but He sits in the temple of human Heart. Thus by worshiping God, we don’t worship someone outside of us but instead be bring out the divinity within us and slowly realise that in the process of reaching a state of infinte we have actually emerged infinite, realised our true self, our true supreme state of consciousness which is beyond the sates of happiness and sorrow.
PS: I am not a true authority on commenting anything on the benefits of Laita Sahastranam. I am her child, and as is natural love to appreciate her. Her glory and true nature can never be described by anyone as She is beyond the reach of the mind and intelligence. Only a person with pure heart and pure emotions can experience her love.
May, Divine Mother who is always gracious and happy, be graceful on all.