<p>Having briefly looked at Haskell recently, what would be a <em>brief, succinct, practical</em> explanation as to what a monad essentially is?</p>

<p>I have found most explanations I've come across to be fairly inaccessible and lacking in practical detail.</p>

But,
You could have invented Monads!
sigfpe says:
But all of these introduce monads as something esoteric in need of explanation. But what I want to argue is that they aren't esoteric at all. In fact, faced with various problems in functional programming you would have been led, inexorably, to certain solutions, all of which are examples of monads. In fact, I hope to get you to invent them now if you haven't already. It's then a small step to notice that all of these solutions are in fact the same solution in disguise. And after reading this, you might be in a better position to understand other documents on monads because you'll recognise everything you see as something you've already invented.
Many of the problems that monads try to solve are related to the issue of side effects. So we'll start with them. (Note that monads let you do more than handle side-effects, in particular many types of container object can be viewed as monads. Some of the introductions to monads find it hard to reconcile these two different uses of monads and concentrate on just one or the other.)
In an imperative programming language such as C++, functions behave nothing like the functions of mathematics. For example, suppose we have a C++ function that takes a single floating point argument and returns a floating point result. Superficially it might seem a little like a mathematical function mapping reals to reals, but a C++ function can do more than just return a number that depends on its arguments. It can read and write the values of global variables as well as writing output to the screen and receiving input from the user. In a pure functional language, however, a function can only read what is supplied to it in its arguments and the only way it can have an effect on the world is through the values it returns.