Put simply, Ethereum Classic provides a way to manage digital assets without the need for intermediaries, such as banks and other financial institutions.
ETC allows uncensorable smart contracts to be written, deployed and executed; it enables truly unstoppable programmable money.
Ethereum Classic is the continuation of the original non-forked Ethereum (ETH) chain and exists to preserve the principle of "code is law".
To find out more about ETC's history and where it's going, check out the Ethereum Classic roadmap.