talking about free monads

No, seriously, can anybody kind of explain to me when they exist?

Have a category C, and endofunctor F, M(F) = fixpoint of (Id + F∘M), right?

Ok, let C be complete, cocomplete, so what? Where's the free monad? Meaning, how come it's a monad at all?

Am I missing something? I don't want a "for example", it's not a proof.