Ethereum Classic is called "Classic" because it is the "original" Ethereum blockchain. It is a long story, but the more popular Ethereum (ETH) is actually a fork/split of the original Ethereum (ETC). The split was the reaction of large theft of Ethereum that happen at an exchange.
The majority of the Ethereum community at that time were ready to accept the fact that the theft had happened and were ready to overcome what ever damage the theft might have caused. There was also a small minority that held most of the wealth of Ethereum and they wanted to protect their wealth at all costs. So they decided to split off of the original Ethereum blockchain and create what we know today as Ethereum (ETH).