The EitherIO data type given is

  data EitherIO e a = EitherIO {
      runEitherIO :: IO (Either e a)
  }

But, for the sake of clarity, it can be written as

  data EitherIO e a = MakeEitherIO {
      runEitherIO :: IO (Either e a)
  }

The author pointed out two functions that this EitherIO declaration gave us. One is a constructor, MakeEitherIO, with type

  IO (Either e a) -> EitherIO e a

In other words, MakeEitherIO takes a value of type IO (Either e a) and returns a value of type EitherIO e a (you could think of this as "wrapping" the original IO value).

The second function, runEitherIO, is an accessor function for EitherIO's named record field "runEitherIO". It has type

  EitherIO e a -> IO (Either e a)

That is, runEitherIO takes a value of type EitherIO and returns the internal value of type IO (Either e a) (you could think of this as "unwrapping" the IO value).

I hope that helps!