There are two fundamentally different types of statement: statements of fact which describe the way that the world is, and statements of value which describe the way that the world ought to be. The naturalistic fallacy is the alleged fallacy of inferring a statement of the latter kind from a statement of the former kind.
Arguments cannot introduce completely new terms in their conclusions. The argument, “(1) All men are mortal, (2) Socrates is a man, therefore (3) Socrates is a philosopher” is clearly invalid; the conclusion obviously doesn’t follow from the premises. This is because the conclusion contains an idea—that of being a philosopher—that isn’t contained in the premises; the premises say nothing about being a philosopher, and so cannot establish a conclusion about being a philosopher.
Arguments that commit the naturalistic fallacy are arguably flawed in exactly the same way. An argument whose premises merely describe the way that the world is, but whose conclusion describes the way that the world ought to be, introduce a new term in the conclusion in just the same way as the above example. If the premises merely describe the way that the world is then they say nothing about the way that the world ought to be. Such factual premises cannot establish any value judgement; you can’t get an ‘ought’ from an ‘is’.
Examples
(1) Feeling envy is only natural.
Therefore:
(2) There’s nothing wrong with feeling envy.
This argument moves from a statement of fact to a value judgement, and therefore commits the naturalistic fallacy. The argument’s premise simply describes the way that the world is, asserting that it is natural to feel envious. To describe the way that the world is, though, is to say nothing of the way that it ought to be. The argument’s conclusion, then, which is value judgement, cannot be supported by its premises.
It is important to note that much respectable moral argument commits the naturalistic fallacy. Whether arguments of the form described here are fallacious is controversial. If they are, then the vast majority of moral philosophy commits a basic logical error.