The character of Caliban is generally thought (and justly so) to be one of the author's masterpieces. It is not indeed pleasant to see this character on the stage, any more than it is to see the god Pan personated there. But in itself it is one of the wildest and most abstracted of all Shakespeare's characters, whose deformity, whether of body or mind, is redeemed by the power and truth of the imagination displayed in it. It is the essence of grossness, but there is not a particle of vulgarity in it. Shakespeare has described the brutal mind of Caliban in contact with the pure and original forms of nature; the character grows out of the soil where it is rooted, uncontrolled, uncouth, and wild, uncramped by any of the meannesses of custom. It is "of the earth, earthy." It seems almost to have been dug out of the ground, with a soul instinctively superadded to it answering to its wants and origin. Vulgarity is not natural coarseness, but conventional coarseness, learned from others, contrary to, or without an entire conformity of natural power and disposition; as fashion is the commonplace affectation of what is elegant and refined without any feeling of the essence of it.
[Hazlitt: Characters of Shakespeare's Plays.]
Oscar Wilde quotes Caliban in two statements in the preface of Dorian Gray. The statements are: "The nineteenth century dislike of realism is the rage of Caliban seeing his own face in a glass" and "The nineteenth century dislike of romanticism is the rage of Caliban not seeing his own face in a glass".
Realistic writers were interested in reaction, logic, and scientific observation. They tried to render reality closely and in comprehensive detail. One aspect of Realism that completely differs from Romanticism is that in Realism there are no characters that overcome insurmountable to be heroes and save the day.
Romanticism was as an artistic movement that took place during the eighteenth century. Romantic writers had a very different style than the normal writers of the time. They stressed the examination of inner feelings, emotions, and use of imagination. They also stressed an accent on the mysterious, strange, and fantastic aspects of the human experience. The last element of Romanticism is an intense reverence for nature and concern with the experience of the individual over the universal.
Wilde expresses trough metaphor and irony that, thanks to realism Caliban would succeeds in watching himself in a mirror and thanks to romanticism he wouldn't see his own face in a mirror, because in romanticism feelings are more important that appearance.