The Uncharted Forest is an instance of a motif that recurs in dystopian literature, representing a forbidden place to which the protagonist is drawn as a symbol of the elements missing from, or contradictory to, the dystopian society.
Equality-7 does not genuinely "fear" anything in the way others do, and in this, he's typical of Ayn Rand's heroes. He is however caught between his own nature and the mentality the authorities have drummed into him and everyone else. The Forest is an unknown place, as distant from the world as another planet in the collective mind of Rand's future society. Despite the superhuman qualities with which she imbues her protagonists, it would be contrary to human nature for Equality-7 not to feel trepidation about a thing so demonized and forbidden.
The Forest is the old, uncorrupted world that existed before the cataclysm resulting in the dystopian society. It is interesting that Ayn Rand's political and philosophical views were the opposite of those of famous dystopian writers such as Jack London, Aldous Huxley, George Orwell, and others, but the literary elements of Anthem are remarkably similar to those of their novels. In Orwell's 1984, Winston discovers (or thinks he does) a world apart from the Party's dominance, in the prole neighborhood and the room above Mr. Charrington's shop. The proles, at least in Winston's thinking, represent "the past," the world that existed before the Party's dominion began. But the refuge Winston and Julia think they have found is a ruse. Their supposed sanctuary there is the beginning of their end. Rand differs from Orwell and the other writers in being an optimist. Her aesthetic theories explicitly denounced literature that showed man as defeated—as a victim. In Anthem, the escape to the Uncharted Forest represents salvation for her protagonists, Equality-7 and the Golden One. It functions as a new start for man and a reverse of the expulsion of Adam and Eve from paradise.