Hard Fork is a considerable update (change) that must be made to a system, especially in crypto currencies. Bitcoin Hard Fork means that this system changes in the scope of the Core Bitcoin (Bitcoin Classic) system. Usually, Hard Fork is only done if the node in the Core Bitcoin network cannot validate a new, valid block, because there is a difference between the nodes that have used the new Core Bitcoin consensus protocol, and the old ones.
The consensus difference occurs permanently, whereas in every new block on bitcoin that the miner must validate there are hundreds to thousands of transactions. This becomes very dangerous, and the only way to go is with a Hard Fork.