Programmers without a mathematical background will naturally struggle with such concepts. You can't point to where in the the code "the monad" is, as it's just the pattern, or the abstract mathematical combination of the type and the operations. Sure you could pack them into a class or a module, but it's still hard to point to where "the monad" is.
When we describe other patterns, like a Singleton, Factory, an Adapter, etc., it's is much more clear what and where the thing is. It's just a word to describe a function, a class, or a module.
Perhaps 'function composition with metainformation' would be a better title for the pattern. You take composable functions that act on certain types, and extend them to support metainformation attached to the values, while defining how the metainformation combines.