Kevala literally means peculiar, exclusively alone, sole, isolated. The atman (being), according to Samkhya, Yoga, Nyaya, Vaisesika and Mimamsa Schools of Indian philosophy, as also the Jains, is separate in each living being, eternal, absolute, pure and isolated. Hence, it is called kevala.
The Jainas call an individual who has come to realize the true nature of the soul a kevalin, i.e. a person having kevala jnana. His atman, after the death of the body, transcends the lokakasa (world of experience) and abides eternally in the alokakasa in full freedom from karma. Here, the atman regains its infinite qualities. The Buddhists do not believe in any transcendental existence for the atman after nirvana, which is a state of niranvaya nasa, i.e. total annihilation, leaving no trace behind. This is in keeping with the Buddhist doctrine of Nairatmya.
On liberation (moksha, mukti, apavarga or kaivalya) this separate kevala (absolute) existence of the atman, wholly unrelated to anything else, is re-established. This view about the soul is very different from that of the Vedanta, according to which the atman is Brahman, just as a wave is in no way different from the ocean or as an ornament from gold.
Kaivalya is the state of the atman as viewed by Samkhya and Yoga, when it is freed from samyoga (togetherness) with antahkarana (internal organ). As mentioned in Samkyakarika (68), in that kevala state the atman remains forever in total isolation. Hence it is called kaivalya. It is a state of pure, absolute existence,devoid of any relation with anything else.