A "monostate" in the design-patterns lingo of 20 years ago was a class with only static member variables, basically where all state is shared state. It was supposed to be alternative to the Singleton pattern where you don't need all those .getInstance() calls and instead can just default-construct an instance, any instance, to get access to the shared state. It fell out of favor because usage was fairly error-prone and surprising to programmers who are not familiar with the pattern. Most people expect that when you create a new instance, you are actually creating new state, but monostate intentionally makes each new instance just a window on the shared global state.

I would've thought that the C++ template class would be just a marker interface to use on a monostate, so that users of the class know that it has shared state. But it seems like usage patterns in the article are very different from that, and all the comments here are ignorant of the history of the monostate pattern and befuddled at its intended usage. Maybe it was added to the standard by someone familiar with the design pattern, but they didn't do a good job with education and documentation to explain to everyone else what it was for?