The Lalitha Sahasranamam is one of the important and famous hymns in the Hindu way of life.  It occurs in the Brahmanda Purana. It is a hymn that describes the 1000 various names of Sri Lalitha Tripurasundari as the Divine Mother. While doing so, the hymn provides a beautiful mix of poetry, romance, religion and philosophy. It is presented during the course of instructions imparted to Sage Agasthya by Lord Hayagriva who is an incarnation of Lord Vishnu.  
Broadly, the Sahasranamam describes the beauty of the Goddess, her kingdom known as Sri Puram or Sri Nagara, the great lotus forest known as Mahapadma vana at the centre of this city of Sri Nagara and her ultimate battle against Bandasura and his annihilation.
I have divided the subject into sixteen chapters and tried to briefly explain it to the extent of my understanding.