I'm not sure what to say about this chapter. It is yet another story-within-a-story in this book, and as far as I can tell it has no direct or implied connections to the larger story of Anodos's journey through Fairy Land. I suppose one could draw connections between Cosmo and Anodos (indeed, this is somewhat implied when the author states that Anodos "was Cosmo"), principally because Anodos is described as a singer, while Cosmo is described as a poet. They both fall in love with a distant, almost abstract woman, who becomes a figurative muse for both characters. The Princess is described as being "a form more like marble than a living woman".
But in my opinion this connection is very strenuous, because this character arc, falling in love with a distant woman and through sacrifice earning her love, is pretty much repeated by nearly every author who has ever written a book. It's the story of human life, especially when you interpret it figuratively and let the woman represent an abstraction, such as artistic perfection, as is the case with the Marble Lady.
Cosmo's description of the mirror parallels Anodos's description of how "all mirrors are magic mirrors", that you can behold something plain with your eyes, yet if you look at the same thing in a mirror it has a grace and beauty about it.
Other than that, I must regard this as almost a separate story altogether. Perhaps that is how it is meant to be regarded. It is certainly a very creative story, with great character descriptions. There is Cosmo, this poor yet proud philosopher-poet, who one day accidentally discovers his muse, the nameless woman who enters his room and his life without choice.
He, of course, falls in love with her (as every man is wont to do), and what I love about the story is how MacDonald presents the decision between possessiveness (using the mirror as power over the lady, to compel her) vs. sacrifice (destroying it, which ultimately costs him his life). I think this is the core of the story, and it's what the mirror is about and Cosmo's sacrifice.
I love how MacDonald describes Cosmo as "falling in love with a shadow", because that's really what it is and that is what so many people do. We fall in love with the impressions and first appearances (and indeed, a shadow is just the impression that our body casts on the ground by blocking out some light). We, humanity, have such a strong tendency to falling in love with the very tiny fraction of a person we get to know, like their appearance or their taste in movies, without ever having the opportunity or the ability to fall in love with their substance, the deeper things of the heart.
Yet while most people will not make any sacrifices for a shadow (as they love too little), in the end Cosmo proves himself by giving up his life to destroy the mirror, to destroy his power. He gave up his ability to manipulate her and laid down his life to buy her freedom.