Someone linked to this illustrated introduction in another thread: http://adit.io/posts/2013-04-17-functors,_applicatives,_and_...

It should give you an idea of what monads are, but probably won't tell you why they're useful. They pop up in lots of places in programming, but you might not notice them at first because most languages have a way around them. They're more explicit in Haskell because the type system is powerful enough to make them both explicit and easy to use, via the combination of parametric polymorphism and type classes.

Here are some examples of monads:

  * Option types (sometimes called nullable types).
  * Many kinds of collections: lists, arrays, trees (but not sets, strictly speaking, because some invariants don't hold when treating sets as monads).
  * Types with logging attached (Writer monads).
  * Continuations.

Furthermore, Haskell's list comprehensions can be thought of as syntactic sugar for monadic operations, in addition to the usual do notation.

Monads are useful because they let you add context to normal values -- any context you want, really. Often, the context just gets called "state", but lots of things are state, really. The monad operations are also useful because they allow you to force a sequence of execution, which is partly why they're also so useful for performing IO: Haskell is designed so that the compiler may re-order operations when it makes sense, and bind lets programmers place a sequential order on parts of the code. This is why the "pipeline" analogy is sometimes used.

An excellent article on monads is "You Could Have Invented Monads", which guides you through discovering several different monads using practical problems: http://blog.sigfpe.com/2006/08/you-could-have-invented-monad...

As for pg, monads don't pop up too often in untyped languages. While you can implement the monadic operations in an untyped language, it makes much less sense to do so. This is especially true for impure languages such as Lisp.