An explanation of the preface in "The Picture of Dorian Gray"

The highest as the lowest form of criticism is a mode of autobiography.

An autobiography is a piece of writing about oneself.

A piece of writing that is really about oneself, or revealing of oneself, we can therefore figuratively call autobiography.

It would be accepted by many that bad writing on a variety of topics are really this sort of autobiography, including works of criticism. That is, "the lowest form of criticism is a mode [type] of autobiography".

Wilde claims that this is in fact true of all criticism, that it all reveals more about their author than it does about the piece they are critiquing.

The nineteenth century dislike of Romanticism is the rage of Caliban not seeing his own face in a glass.

Wilde has given you a context that you have left out here. A fuller quote is:

The nineteenth century dislike of realism is the rage of Caliban seeing his own face in a glass.

The nineteenth century dislike of romanticism is the rage of Caliban not seeing his own face in a glass.

And we'll examine the first sentence of these two first.

Now, Caliban is indeed a character in a Shakespeare play, specifically "The Tempest". A fuller understanding of the phrase will come from reading or (better) watching this play, and perhaps also being familiar with what others have had to say about him.

That will take too long, so for now let me just say that Caliban is a sub-human or part-human monster, capable of reasoning and language, but also physically ugly and immoral and base in his actions. Yet for that, he is at least partly a sympathetic character, at the mercy of his nature—we fear him in his rage and his plotting to overthrow the hero and rape his daughter, yet also we pity him in his deformity and his impotence.

And so too does Caliban pity himself. It is at least a possible reading that what makes Caliban angry is not Prospero's treatment of him, but his awareness of his own base nature. He is described as being to a man as man is to an angel, and he is in fact what man is when man compares himself to angels, or to any other ideal of what man can be. He is what we do not like about ourselves when we examine ourselves.

And he does not like what that examination shows. So:

The nineteenth century dislike of realism is the rage of Caliban seeing his own face in a glass.

19th century readers do not like realism, because they show that reader uncomfortable truths about themselves (both as individuals and as a society) that they are not prepared to deal with.

And that statement made, the next is a deliberate contrast:

The nineteenth century dislike of Romanticism is the rage of Caliban not seeing his own face in a glass.

Just as readers cannot handle what shows them reality, so too they cannot handle what does not.

There has been, and continues, a debate as to whether, how and to what extent art should reflect life. Wilde is being disdainful of both sides in saying that the artist who reflects life will be rejected for doing so, and the artist who does not reflect life will be rejected for not doing so.

This preface as a whole is not the easiest passage generally; dense, contradictory, and expectant of an audience interested in current literary debates. I would note that the story itself is not as difficult as this preface, and one need not understand this preface to enjoy it.