Sort of like NULL, especially in that both NULL and Nothing mean "the absence of a value" and cannot be combined or compared with anything else. But it goes way beyond that.

Think of Maybe as a container. It either "contains" a value, or it doesn't. The container itself is not usable except for passing around; it's the contained value that is important. Even if we know that the container is supposed to contain a number, we can't use the container to perform computations; every time we need the number, we need to open the container, peek inside, and decide what to do whether it's contains something or nothing.

In Haskell terms, this "peeking inside" is typically done with pattern matching, which is core to the type system. For example, this is a function that checks if a Maybe value has anything, and returns true or false:

hasValue x =
case x of
Just _ -> True
Nothing -> False

The line "Just _" is a kind of wildcard expression, meaning: "Check if x matches the pattern Just [something]".

At the opposite end, we can have functions that produce Maybes (naive and simplified example, not working code):

fetchPage url =
do response <- performHttpRequest "GET" url
case (getStatusCode response)
200 -> return (Just (getBody response))
404 -> return Nothing

Notice how "Just" looks like a function call. That's because it is. It's a function that "constructs" a value of, in this case, type "Maybe String". The "Nothing" returned is also a value of type "Maybe String". Thanks to Haskell's type inference, this is known at compile time.

In languages such as Java or Ruby we can build classes that are containers that act in a similar way. But those languages are limited in that "peek inside the container" logic needs to happen at runtime. In Haskell, the container's possible values are enforced entirely by the type system at compile time.

To really appreciate this, you really have to be familiar with statically typed languages such as C++ or Java. In such languages, you have "nil" or "null" or "NULL" values to represent "nothing". Any time you have a pointer, you have to explicitly check if the pointer is valid; if you try to use it, and it happens to be null, the program will blow up at runtime, but not at compile time.

In Haskell, there is no generic null value. The value "Nothing" on its own belongs to a specific type, such as "Maybe String", and won't work with another such as "Maybe Integer". Thus when we want to use "fetchPage", we are forced into a situation where must make a choice based on whether there is a value or not (again, naive example):

crawlPageRecursively url =
do contents <- fetchPage url
case contents of
Just s -> map crawlPageRecursively (map (\body -> getLinks body) s)
Nothing -> putStrLn ("Failed to fetch " ++ url)

Since Haskell doesn't have null pointers, and can never end up in a situation where you try to use a null where you expected a value, because its type system makes it impossible.

This was my attempt at "explain it like I'm five" Haskell as carefully as I could. The real world is somewhat more complex, but not awfully so. As you say, too often haskellers will get into "formal academic theory", even when, in my opinion, it's not necessary. Haskell becomes more elegant and beautiful if you study and know group theory, but most people don't, and it really just obscures the language for ordinary, mortal programmers who are trying to learn it.

As for monads, it's true that Maybe is a monad, but think of it as a convenience, in the sense that this lets it play well with the rest of the monad infrastructure. You can use, and even implement, Maybe without involving the monad aspect.

My best suggestion regarding monads is to just start using the language; as DanWaterworth points out, monads are pretty much inexplicable for beginners until one really needs to use them. Haskell actually lets you use some monads (like IO) without requiring any deep understanding of what they are. Case in point: The above examples actually use the IO monad, concealed by the "do" and the "<-" syntax. But because this syntactic sugar makes the language look like an imperative language, you can use this stuff without too much deep knowledge about just exactly how it works under the hood.