From my limited understanding garnered by listening to SE Radio, monads are basically a way for Haskell programs to execute actions (rather than simply computing values), so that your program can ultimately DO something like write to a file. As you probably know, the functions aren't supposed to contain any side effects: you don't want something unexpected to happen when you just want to calculate a value. It would be like a spreadsheet that printed out a page every time you entered a certain cell - might make sense in a one-off situation but in the long run it's just inviting trouble.

So monads allow sequences of actual actions to be packaged together and given preconditions and then executed in a safe manner (perhaps with an eye to concurrency). You get to maintain the exquisite purity of functional programming while still writing software that, you know, gets stuff done occassionally.

If you were looking for an explanation of the mathematical concept though, sorry, ain't got a scooby.