Swayamprakasha means self-luminosity. The ultimate Real (Brahman or atman), according to Advaita Vedanta, is of the nature of sat (existence), jnana (consciousness)a and ananda (bliss). This ultimate reality is considered to be self-revealing or self-luminous – Swayamprakasha.
A self luminous principle is one which manifests other objects but which, on the other hand, does not require any other factor for its own manifestation, i.e., it stands self-revealed. In other words, it reveals its own self as well as the objects that come in contact with it, much like a lamp.
The concept of self-luminosity has been deal with by many preceptors of Advaita. One of them, Citsukha, defines and elaborates it in his Tattva Pradipika as aparoksha vyavahara yogya (capacity of being graspable), while not being an object of cognition (avedyatva). Three factors are involved in a cognitive process, viz., the object cognized, the mental modification of the form of the object (called vritti) and the enlightening principle of consciousness. It is because of the last factor that objects are cognized.
The self-luminosity of atman is set forth in the Upanishads like Brihadaranyaka Upanishad (4.3.9, 4.3.23), Chandogya Upanishad (3.14.2), etc., where it is said the self of atman is self-luminous and it is by its light that all others shine. This self luminous principle (called jyotisha, atman or Brahman) illuminates the Universe born out of avidya (ignorance) and removes the darkness of ignorance, as sunlight illuminates the world by dispelling the darkness of night. And realization of its true nature is considered the summon bonum of existence.