Sure. This is probably a much more useful question than "what".

For Haskell, Purescript, Agda, Idris and other languages that like to rely on them, Monads represent some cool properties that make code extremely reusable.

1. Monads have a uniform, universal description of sequenced code. They can model essentially any form of computation that depends on its input and known state. This makes them a very nice level of abstraction to write highly generic tools.

As an example I wrote about here awhile ago (https://news.ycombinator.com/item?id=16831985), it makes it easy to write async code execution strategies without ever even considering any aspect of the code other than that it's sequenced.

2. Monads describe behaviors, but a subtle point is that in a language with generic code (paramaterized or higher-kinded types, etc.) Monads let you write code to a GENERIC monad.

As an example, what does this code do?

    data SomeThing = SomeThing { name :: Text, age :: Int }
    
    makeSomeThing :: (Monad m) => m Text -> m Int -> m Something
    makeSomeThing nameE ageE = do
        name <- nameE
        age <- ageE
        return $ SomeThing name age

This code Makes SomeThing (and yes, I could write this more neatly as `liftM2 SomeThng`, and often we use Generics to mechancially derive this code, but I'm making a point here). But we haven't discussed anything except that:

a. We are given effects to get name and age.

b. We seqentially use those effects to produce two values.

c. We then have an effect to produce SomeThing.

That's pretty amazing, if you think about it. Depending on what the monad is, we could be calling over the network, or executing things in parallel, or parsing it off of stdin. We could use the Maybe monad to represent values that may be missing, or we might use Envy (https://hackage.haskell.org/package/envy) to read it from the environment.

Monads give you a way to parameterize the structure of the logic you need to describe a task and make statements within that logic.

This is why monadic programming tends to get really addictive. And as time has gone on, everyone has found new compiler techniques to make this kind of code easier AND more powerful.

The next generation of programming languages folks are researching focus on Dependent Types (hi Agda and Idris) and Linear types (hi Rust and Pony and Idris), which let us take monads even further, allowing for a princpled approach even with previously complex tricks like interleaved effects, sophisticated type indexes, and consistent resource management.

> Edit: like the two things I spend most of my day writing code for are UI stuff and database code - can monads do anything for me there?

I just posted this code elsewhere, I just wrote a for-production Haskell microservice that I made generic over the database actions (type "p" in the code). This code does not know what database OR header validation scheme it's going to use, only that we've explained how to make CanValidate and Patchable actions in our action monad. This is better than writing for DI or mocking, DI and mocking usually couple your tests and underlying code structure deeply. This is Faking, where I have a trivial alternative service stubbed in so I can test my API logic without appealing to a database, and then run integration tests on my database actions separately.

https://gist.github.com/KirinDave/9b4380376f9f748bcf0f8440de...

You might also see that I have "ValidAction" and "BaseAction" and there is a "validationHook." The framework I chose here lets me use "hooks". These hooks help the compiler check that I only run my database actions inside a Validated context, and don't try to validate again once I've already Validated. More precisely, they're helper functions to let us pretend indexed monads are normal monads.

Here are sample implementations of CanValidate and Patchable from unit tests from that code so you can see the constraints in play.

https://gist.github.com/KirinDave/fe317bffb5e4b2f1316c207325...