In computer science, we can squint and claim that a functor is just something that has a .map function, taking a function. Option, Promise, List... all functors.
The fact that functor is a concept, and follows specific laws, allows us to have other abstractions that work across all functors without having to repeat ourselves over and over again. See, for instance, Scala's for comprehension. it offers different iterating capabilities over basically anything, and it will give you more capabilities if instead of just functor, you pass a monad, or something that supports .filter.
Also see the possibilities of generic transformations. Every language that supports Promise needs some way to turn a list of Promises into a Promise holding a list, and vice versa. We can do this with options, or Eithers, or some home-made thing that is holding on to any other property we like... but it's so much easier to do so without having to write every possible combination of two things, and rely on the fact that one might be a monoid, or a monad, and not have to write all the boilerplate.
In languages that take this very seriously, you can do things like, say, apply a tracing library to an http request, or a logger, or manage creation of resources, all throught category theory concepts, and have all the wiring basically disappear, instead of havign to either pass a million parameters, or relying on some dubious Aspect-oriented-programming instrumentation that might or might not work. All visible, and checkable at compile time. And you get there by making all your abstractions are functors, monoids, monads and such.
The fact that functor is a concept, and follows specific laws, allows us to have other abstractions that work across all functors without having to repeat ourselves over and over again. See, for instance, Scala's for comprehension. it offers different iterating capabilities over basically anything, and it will give you more capabilities if instead of just functor, you pass a monad, or something that supports .filter.
Also see the possibilities of generic transformations. Every language that supports Promise needs some way to turn a list of Promises into a Promise holding a list, and vice versa. We can do this with options, or Eithers, or some home-made thing that is holding on to any other property we like... but it's so much easier to do so without having to write every possible combination of two things, and rely on the fact that one might be a monoid, or a monad, and not have to write all the boilerplate.
In languages that take this very seriously, you can do things like, say, apply a tracing library to an http request, or a logger, or manage creation of resources, all throught category theory concepts, and have all the wiring basically disappear, instead of havign to either pass a million parameters, or relying on some dubious Aspect-oriented-programming instrumentation that might or might not work. All visible, and checkable at compile time. And you get there by making all your abstractions are functors, monoids, monads and such.