Monads don't have anything to do with laziness but historically the need for them arose because of laziness. It's the first thing explained in the introduction of Tackling the Awkward Squad:
"Call-by-need (or lazy) languages, such as Haskell, wear a hair shirt because their evaluation order is deliberately unspecified. Suppose that we were to extend Haskell by adding side-effecting “functions” such as printChar. Now consider this list
xs = [printChar 'a', printChar 'b']
(The square brackets and commas denote a list in Haskell.) What on earth might this mean? In SML, evaluating this binding would print 'a' followed by 'b'. But in Haskell, the calls to printChar will only be executed if the elements of the list are evaluated. For example, if the only use of xs is in the call (length xs), then nothing at all will be printed, because length does not touch the elements of the list.
The bottom line is that laziness and side effects are, from a practical point of view, incompatible. If you want to use a lazy language, it pretty much has to be a purely functional language; if you want to use side effects, you had better use a strict language.
For a long time this situation was rather embarrassing for the lazy community: even the input/output story for purely-functional languages was weak and unconvincing, let alone error recovery, concurrency, etc. Over the last few years, a surprising solution has emerged: the monad. I say “surprising” because anything with as exotic a name as “monad” — derived from category theory, one of the most abstract branches of mathematics — is unlikely to be very useful to red-blooded programmers. But one of the joys of functional programming is the way in which apparently-exotic theory can have a direct and practical application, and the monadic story is a good example. Using monads we have found how to structure programs that perform input/output so that we can, in effect, do imperative programming where that is what we want, and only where we want. Indeed, the IO monad is the unifying theme of these notes."
"Call-by-need (or lazy) languages, such as Haskell, wear a hair shirt because their evaluation order is deliberately unspecified. Suppose that we were to extend Haskell by adding side-effecting “functions” such as printChar. Now consider this list
(The square brackets and commas denote a list in Haskell.) What on earth might this mean? In SML, evaluating this binding would print 'a' followed by 'b'. But in Haskell, the calls to printChar will only be executed if the elements of the list are evaluated. For example, if the only use of xs is in the call (length xs), then nothing at all will be printed, because length does not touch the elements of the list.The bottom line is that laziness and side effects are, from a practical point of view, incompatible. If you want to use a lazy language, it pretty much has to be a purely functional language; if you want to use side effects, you had better use a strict language.
For a long time this situation was rather embarrassing for the lazy community: even the input/output story for purely-functional languages was weak and unconvincing, let alone error recovery, concurrency, etc. Over the last few years, a surprising solution has emerged: the monad. I say “surprising” because anything with as exotic a name as “monad” — derived from category theory, one of the most abstract branches of mathematics — is unlikely to be very useful to red-blooded programmers. But one of the joys of functional programming is the way in which apparently-exotic theory can have a direct and practical application, and the monadic story is a good example. Using monads we have found how to structure programs that perform input/output so that we can, in effect, do imperative programming where that is what we want, and only where we want. Indeed, the IO monad is the unifying theme of these notes."
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