I generally think of non-cognitive statements as statements which do not 'aim to describe the world'. i.e. when you make the statement, you are not making a factual claim which can be empirically verified. When you say 'I like Star Trek', you are referring to a feeling you have when watching Star Trek, this is something which cannot be 'pointed' to in the world and claimed to be true or false. Sure, someone could look inside your brain and see you are undergoing the appropriate activity as if you were enjoying something, but this isn't the same as proving the feeling, it is ignoring the idea of qualia.
Not sure if that made much sense, but that's how I think of it. So if you were claiming that moral statements were non-cognitive, you would claim that they do not aim to describe the world (you can't point at the world and say 'there's goodness!'), and therefore cannot be true or false as they cannot empirically verified.