Background and further Reading

Concepts like functor and monad have their origin in category theory, a branch of mathematics. That is also where their laws come from. Category theory was found to have applications in programming language theory, especially functional programming. It is a highly abstract topic, but there is a pretty accessible introduction for programmers, written by Bartosz Milewski.

The usefulness of applicative functors as a middle ground between functor and monad was discovered several years after monads had already been in use in Haskell. They were introduced in the article Applicative Programming with Effects, which is freely available online and a highly recommended read.