It’s a “programmable semicolon” or “decorated-function composition”

"programmable semicolons" is wrong, you can have that without Monads, and in fact Haskell has a do-notation for Applicative. "decorated function composition" is a bit vague, I think I see what you mean but it's not too helpful.

It's just an interface for a generic type that requires two specific functions to be implemented. Understanding why it is so useful is the tricky part.