What does “the eyes of them both were opened” (Gen 3:7) actually mean?

The short answer is: they immediately became aware that they had violated God’s commandment, and that fact alone made them aware of the evil within themselves and the serpent who had misled Eve. More profoundly, their eyes were opened to the deceptive pleasures and unexpected pains of a fallen world in which they were left to their own devices. Let me explain. We can take some clues, at least, from the context. This knowledge is forbidden by a God who has their welfare at heart, but who also does not want them to become “like gods,” as was the ambition of the men of Babel whom God threw into confusion (Gen 11:1-9). The knowledge immediately lets them know that they are naked; but since God allowed them in his holy presence to go about naked, the knowledge seems at the same time to have made their nakedness shameful. Finally, we can say the knowledge gave them the ability to handle the harsh penalties imposed upon them by God. Given that it is called “the knowledge of good and evil,” one is tempted to say that it is the rational, adult ability to discern moral goodness from evil; after all, the naive, newly-created Eve certainly lacked such discernment in her encounter with the serpent, and ever after, there would be “enmity between [the serpent] and the woman” (Gen 3:15). But I am not sure sure about the latter suggestion; I think more likely is a suggestion I read in one commentary, that “good” and “evil” here are not meant in their moral senses but in the sense of blessing versus curse. To eat of the tree would give them knowledge of the cursedness of the world, and the natural consequence was that the world was cursed; it had to be, for them to have knowledge of the evils of such a world. And after all, previously, it was “very good.”