Abhaya means fearlessness and it is a cardinal virtue extolled in Hindu texts. It is also the goal of all spiritual endeavors in Hinduism. In Hindu temple sculptures, gods and goddesses are represented as assuring fearlessness with one hand (abhaya hasta) and showering grace with the other (varada hasta).
Notes taken from Encyclopedia of Hinduism Volume I page 5 (IHRF).
The modern day popular concepts of Ahimsa (non-violence) and satyagraha (non-cooperation) are based on the Hindu concept of Abhaya.
The Bhagavad Gita (XVI – 1) puts fearlessness as the first among divine qualities (daivi sampat).
Abhaya is said to be the same as enlightenment.
Yajnavalkya tells his disciple king Janaka that he has attained fearlessness, thereby indicating his wisdom (Brihadaranyaka Upanishad IV – 2.4).
Taittiriya Upanishad (II. 7.1) says that Brahman is established on the basis of Srishti (creation), rasalabha (experience of happiness), pranana (survival), bhayaabhayahetu (order in the universe) and abhayapratistha (fearlessness). (Taittiriya Upanishad (1962) Swami Chinmayananda
The Upanishad explains that when one sees difference, even to the smallest degree, there arises fear. So long as there is another, there is finitude and hence fear. When the notion of difference is transcended by the vision of underlying unity, there is fearlessness which is moksha (release).
In Hinduism, a person taking to the life of a sannyasi (ascetic) is expected to make a promise that he will spread fearlessness among all beings. In fact, fearlessness is the other side of ahimsa (non-violence). “Injure no being,” states Chandogya Upanishad.
Lord Rama in the Ramayana promises fearlessness to all beings who have surrendered unto him. Thus, fear in the Hindu religion is the mark of divisive notions while fearlessness bespeaks uniting wisdom. Giving refuge to people who are in mortal fear of being killed is considered to be the greatest virtue and hence the greatness of the Ramayana, whose hero had given refuge to all Saranagatas i.e. those who had sought refuge.
Hindu thinkers observe that the cause of fear is raga (attachment), and the conquest of fear needs abandonment of worldly attachment. By practicing vairagya (non-attachment) or tyaga (renunciation) one may acquire absolute fearlessness.
Notes taken from Encyclopedia of Hinduism Volume I page 5 (IHRF).