This is a memorial to Mahatma Gandhi. The black marble cenotaph marks the spot of Gandhi's cremation on January 31, 1948. (The platform is within a walled enclosure. To enter, visitors remove their shoes and pass through a narrow tunnel. Visitors pay respects by placing flowers on the platform. (You can buy the flowers outside of the walls, and one photo shows one of the flower sellers.) We also spoke with a family that had come to pay their respects.
http://en.wikipedia.org/wiki/Raj_Ghat_and_associated_memorials