Ethereum Classic split from the original Ethereum blockchain following a major hacking event that led to the theft of 3.6m ETH on the Ethereum blockchain in 2016. The split occurred when participants of the Ethereum protocol disagreed over whether to revert the blockchain to cancel out the effects of exploiting a weakness in the code of a decentralized autonomous organisation (DAO) smart contract.
While Ethereum reverted the chain, Ethereum Classic did not and on the basis that the smart contract was performing according to what the code states.
Ethereum Classic has the same use case as Ethereum (see also slide “Ethereum”), however both blockchains are drifting apart on a technological level with Ethereum Classic not switching to a proof of stake consensus mechanism for the time being.
Ethereum Classic is the continuation of the unaltered history of the original Ethereum blockchain. The Ethereum Classic protocol exists to preserve the principle of “code is law".