Avyaya means which is never deteriorates. That is avyaya. Vināśam avyayasya asya na kaścit kartum arhati. Nobody can kill. Nobody can kill consciousness, nobody can kill the soul. Therefore it is said, na hanyate hanyamāne śarīre (BG 2.20). "The consciousness, or the spirit soul, is never killed, never annihilated, on the destruction of this body." So this is a great science. Unfortunately, the so-called scientist, he has no idea. He does not know.
Bhagavad-gita As It Is Lectures
So Kṛṣṇa points out that this consciousness is immortal, avyaya. Avyaya means which is never annihilated, avyaya. Vyaya means there is whole thing, and you can take out part of it, but avyaya means you cannot take a part of it also; it is always wholesome. So this consciousness is avyaya, means never annihilated, and avināśi means immortal. So when this consciousness is transferred from this body to another body, that is called transmigration of the soul.
If Kṛṣṇa is the complete, supreme, so even He expands Himself in millions and trillions of complete forms, still, He is complete. Still, He's complete. This is conception of Kṛṣṇa. So therefore avyaya. Avyaya means acyuta, avyaya. Acyuta means He does not fall. It is not like that, that in my bank I have got one hundred pounds; if I take one, two, three, four, five in this way, one hundred finished, my bank balance is finished. It is not like that. Kṛṣṇa is so complete that immediate forms may be expanded from Him; still, He is complete. Pūrṇasya pūrṇam ādāya.
Śrī Caitanya Mahāprabhu, He appeared on this earth five thousand years ago in Bengal, Navadvīpa, to spread this Kṛṣṇa consciousness, although this movement is not new. This Kṛṣṇa consciousness movement was started by Kṛṣṇa Himself. Apparently the Kṛṣṇa consciousness movement was started by Kṛṣṇa Himself in the Battlefield of Kurukṣetra five thousand years ago, and He said that "This Kṛṣṇa consciousness movement I spoke to the sun-god long, long years ago." Imaṁ vivasvate yogaṁ proktavān aham avyayam (BG 4.1). This is avyaya. Avyaya means which is never diminished or destroyed. Vyaya means which is destroyed, and Kṛṣṇa says this yoga system... This is yoga system: bhakti-yoga. Yoga means to connect, to add, yoga. So at the present moment we are almost disconnected. Not exactly disconnected; forgotten our relationship with Kṛṣṇa, or God. God means Kṛṣṇa, and Kṛṣṇa means God. So in the human society there are many different types of yoga system just to reconnect our relationship with Kṛṣṇa.