Self-realization is a concept that has become widely popular in the Western and that has great influence from some Eastern religions. For instance, for the Hindu or Bharat religion self-realization refers to a profound spiritual awakening where there is an awakening from an illusory self identify image (Ego), to the true, divine, perfect condition that the individual is. The branch of Advaita Vedanta is the one that has especially developed this concept.
Furthermore, the method of meditation Sahaja Yoga, created in 1970 by Shri Mataji Nirmala Devi, defines self realization as a connection with your self or the first encounter with reality.
One of the definitions in the Western can be found in Merriam Webster’s dictionary. It defines self-realization as “fulfillment by oneself of the possibilities of one’s character or personality”.
Definition courtesy Wikipedia.