Q: What is Karet?
A: The Alter Rebbe explains the meaning of karet in the end of chapter 5 of Igeret Hateshuvah. Karet means "to sever." It signifies the cutting off of the consciousness of the soul present in the body from its superconscious source which is always at one with G-d. Nonetheless, it is always possible to do teshuvah (repent) and to reconnect–with a stronger bond than before–the finite dimension of the soul with its infinite source. The soul's source then arouses "from afar" the estranged finite consciousness of the soul's reflection in the physical body to do teshuvah. If in a certain life-time the soul does not merit to do teshuvah it will be reincarnated in one form or another until it achieves its rectification. Often the reincarnation in a lower form of life (or even inanimate existence) suffices to achieve the rectification, for the soul's inability to choose is spiritual imprisonment which counteracts the wrong choices of a previous lifetime.
The root of the word karet also means to create a covenant–kritat brit. A covenant is an existential state of being, above and beyond all consciousness accessible through reason and intelligence. Thus, the complete rectification of karet is the renewal of one's essential covenant to G-d, His Torah and His People Israel.
Karet is a permutation of keter, the crown or superconscious level of the soul, whose inner dimension is equivalent to the soul's root above, always united with G-d. Karet blemishes the external dimension of keter (its power of will to perform the will of G-d as revealed in the Torah) but does not affect its inner dimension (the serenity of its absolute union with G-d.)