There is no recognized and official statement of Cornell realism, but several theses are associated with the view.
A common way of explaining the thesis invokes the claim that amoralists are possible – that there could be someone who makes moral judgments without feeling the slightest corresponding motivation.
This gives Cornell realists a simple response to Humean arguments against cognitivism: if moral judgments do not have motivational force in the first place, there is no reason to think they are non-cognitive states.
But while they are not supernatural (as in divine command theory) and they are not non-natural (as in Moore's Principia Ethica or Mackie's picture of a realist world), they cannot be reduced to non-moral natural facts.
This usually goes with a Kripke-Putnam semantic story: moral terms and concepts pick out certain natural properties in virtue of those properties standing in an appropriate causal (social-historical) relation to our tokenings of the terms and concepts.