The definition of a hard fork is not easy, so we’ll better start with an example from the latest hard fork news. A well-known example of a hard fork was the appearance of Bitcoin Cash as an alternative to Bitcoin Classic with improved transaction speed and smaller fees. This schism led to the presence of 2 completely different currencies. The key point of this occasion is those changes are permanent, and that is what differs hard fork from any other changes in the system.
So, a hard fork is a radical change in the Blockchain that makes all the previous blocks or transactions invalid (or vice-versa). Events like this make all users upgrade their software to the latest version, because previous versions become unusable in the newest one. This event creates a split or a fork: one path follows the new version and one path follows the old one.