What does the => sign mean in Haskell?

The type signature

sendMessage :: MonadM e m => Message -> m ()

can be read

Assuming that the constraint MonadM e m holds, sendMessage has type Message -> m ()

MonadM is (almost certainly) a multi-parameter type class with a functional dependency. Its definition probably looks vaguely like

class Monad m => MonadM e m | m -> e where ....

You don't have to worry about that right now. Writing such classes is a somewhat advanced topic. But it expresses that some operations are available that relate the types e and m, where the type e is determined by the type m.

First off: if you want to know what such and such operator does, don't ask StackOverflow, ask Hoogle!

But in fact Hayoo is no use for => in particular because, unlike almost everything else in Haskell, this is built-in syntax and not an operator that's defined in some library.

Your signature

sendMessage :: MonadM e m => Message -> m ()

means the following: the type of sendMessage is Message -> m (), where m can be any monad that has an instance of the MonadM type class.

That probably doesn't help you much, because in fact MonadM is a rather involved type class. Better consider a simpler example:

sum :: Num n => [n] -> n

This means: the type of sum is [n] -> n, where n can be any number type that's an instance of the Num class, i.e. the class of types supporting subtraction, multiplication, obviously addition etc.. Actually the syntax is shorthand for

sum :: ∀ n . Num n => [n] -> n

meaning that for all types n which fulfill the constraint Num n, the function sum has the signature [n] -> n.

You can instantiate such a polymorphic function with any concrete number type: e.g.

sum :: [Int] -> Int

In your example you'd probably instantiate it to something like

sendMessage :: Message -> MessageT IO ()