We might give a more detailed definition, in terms of propositions and reduction, that, in generalities, expresses the general understanding of the term:
Ethical naturalism combines cognitivism with moral reductionism: as the second part of the above definition says, ethical sentences "can be reduced to nonethical sentences." To say that ethical sentences can be reduced to nonethical sentences is to say that you can state the meaning of ethical sentences in other words, in sentences that do not include any ethical terms like 'good' and 'right'. (See reduction.) In other words, all talk of good and bad, right and wrong, moral and immoral, and so forth, is (ultimately) just shorthand for some complex propositions about what human beings need, or desire, or what gives them pleasure, or what secures their long-term happiness, and so forth. So the notion that ethical sentences can be reduced to nonethical sentences really amounts to saying that ethical sentences are a kind of shorthand, a kind of useful abbreviation, for claims about what are ultimately nonethical facts about human needs, desires, and so forth.
Theory of Value
The theory of value--an important branch of ethics--contains a number of theories of what 'good' means, or (construed differently) of what general sorts of things are good. Hedonism, just to take one example, is the view that goodness is ultimately just pleasure; hedonism is one attempt at giving a theory of value. Therefore, one could look at the theory of value as a way of thinking ethical naturalism through; the theory of value can be regarded as an attempt to figure out how to reduce goodness to nonethical properties. So, if it is initially puzzling how one could ever reduce ethical sentences to nonethical sentences, one need only review the theory of value for many examples of such reductions. We should add, however, that not all philosophers working on value theory would view their theories as reductions.