The State API is a key/value database storage and the simplest way you can store some data in Drupal 8. One of its main purposes is to allow developers to store information that relates to the state of the system (hence the name). And because the state of the system can be interpreted in various ways, think of this as simple information related to the current environment (Drupal installation) that is not editorial (content). An example would be the timestamp of the last time the Cron ran or any flags or markers that the system sets to keep track of its tasks. It is different from caching in that it is not meant to be cleared as often, and only the code that sets it is responsible for updating it.
One of the main characteristics of this system is the fact that it is not designed for human interaction. I mean this in the sense that it is the application itself that needs...