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Blockchains establish consensus by nodes considering the longest valid chain to be the consensus chain. A hard fork is when a client upgrade results in a conflict arising in more than one possible valid chains. Whichever after a fork chain has more than 50% of the hashing power (or whatever alternate security mechanism is used), it will generally grow faster, have more transactions, and be considered to be the consensus chain. Ethereum's hardfork essentially rewrote history to undo the The DAO hack. Someone found an exploit in a contract holding about 10% of total ETH, and move it to another contract. This hard fork reverses that hack, and enables The DAO token holders to revert their tokens back to ETH.