throw is an expression which halts the function and generates an exception. Whatever directly follows throw is passed along in the exception. Think of it as a function with syntax sugar, so instead of writing throw('message') you write throw 'message'. throw new Error('message') is just like throw 'message' except an object is being passed along instead of a string literal.
There is no difference between throw Error('message') and throw new Error('message'): many of the core JavaScript objects allow for the creation of a new object without the new constructor and Error happens to be one of them.
That being said, you should always use throw new Error('message'). The Error object contains a stacktrace and other useful debugging information which is lost when you use a string literal. Creating objects using ES6 classes requires the use of new and extending Error via a class is the only way to preserve stacktraces. Creating a custom error class makes error handling much more uniform.
See Also: extremely elaborate illustration.