‘But, soft! what light through yonder window breaks?’ is a speech made by Romeo at the beginning of Act II Scene 2 in Shakespeare’s Romeo and Juliet. The whole of the speech beginning ‘But, soft! what light through yonder window breaks?’ represents the consolidation and confirmation of Romeo’s love for Juliet, as he echoes his initial paean to her beauty (from Act I Scene 5), but the intensity of his feeling is seen to develop. Before we proceed to an analysis of this passage, here’s a reminder of Romeo’s speech.
But, soft! what light through yonder window breaks?
It is the east, and Juliet is the sun.
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief,
That thou her maid art far more fair than she:
Be not her maid, since she is envious;
Her vestal livery is but sick and green
And none but fools do wear it; cast it off.
It is my lady, O, it is my love!
O, that she knew she were!
She speaks yet she says nothing: what of that?
Her eye discourses; I will answer it.
I am too bold, ’tis not to me she speaks:
Two of the fairest stars in all the heaven,
Having some business, do entreat her eyes
To twinkle in their spheres till they return.
What if her eyes were there, they in her head?
The brightness of her cheek would shame those stars,
As daylight doth a lamp; her eyes in heaven
Would through the airy region stream so bright
That birds would sing and think it were not night.
See, how she leans her cheek upon her hand!
O, that I were a glove upon that hand,
That I might touch that cheek!
‘But, soft! what light through yonder window breaks? / It is the east, and Juliet is the sun …’: Romeo begins this speech when he sees Juliet at her window. (Whether she’s at a balcony is much disputed; the balcony appears nowhere in Shakespeare’s stage directions – Juliet is simply described as being somewhere ‘above’ – and the first production known to use a balcony wasn’t staged until the late seventeenth 
century.)
Still, the idea of Juliet being like the sun rising in the east is a nice one, and picks up Romeo’s earlier description of Juliet (‘O she doth teach the torches to burn bright’).
Having begun with this rhetorical question (‘But, soft! what light through yonder window breaks?’), Romeo offers an extended analogy in which Juliet = the sun. The moon is ‘envious’ of her because it has no radiance of its own: it has to borrow its light from the sun (i.e. Juliet), and resents the fact, like the plain-looking lady who resents her prettier maid who gets all of the romantic attention. Romeo riffs on the paleness of the moon, seeing this as a sign that the moon is ‘sick and pale with grief’ because its ‘maid’, the sun, is more fair or beautiful than she is.
Romeo tells Juliet, the sun, not to be a maid attendant on the moon any more, because the moon is envious of her beauty. Why? Why would the sun be the maid to the moon? Surely, if anything, it should be the other way around?
But no: Shakespeare has in mind the Roman goddess Diana, who was associated with the moon: Diana represented chastity and virginity, so the moon has ‘vestal livery’ because her followers would be like the vestal virgins from ancient Rome who were followers or priestesses of a goddess. Juliet should not follow the cold, distant moon, that represents chastity; for one thing, Romeo probably doesn’t want Juliet to remain a virgin.
After all, when Romeo tells Juliet to ‘cast … off’ the ‘livery’ or clothes of Diana/the moon, he’s essentially telling her to get her kit off …
It is my lady, O, it is my love!
O, that she knew she were!
A nice bit of metrical shortening here, as Shakespeare departs from the regular iambic pentameter and blank verse used in the rest of Romeo’s speech, and gives us just three feet in the line ‘O, that she knew she were!’ (to mirror the longing in Romeo’s voice – the short line brings us up short, as we remember that Juliet doesn’t yet know the depth of Romeo’s feeling for her).
Juliet’s eyes are ‘speaking’ because her expression says as much as words could. Romeo is feeling ‘bold’, so steps forward to ‘answer’ the look in her eyes with a profession of his love. Romeo then likens Juliet’s eyes to two stars in the night sky: it’s as if Juliet’s eyes are bright and beautiful enough to stand in for the stars while they’re off on ‘business’.
Romeo then extends this idea into a poetic conceit: okay, if there were two stars from heaven in Juliet’s head and her eyes were in the night sky, those stars would feel shamed by being so close to the (superior) brightness of Juliet’s cheek, much as a lamp is shamed by the presence of natural daylight. We’re back to her teaching the torches to burn bright again.
Meanwhile, Juliet’s eyes – in heaven, in place of the stars – would shine so brightly that the birds would think it was daytime rather than night. From this bizarre image of Juliet’s disembodied eyes floating in the night sky among the stars, we come to the slightly less fanciful image of Juliet leaning her cheek upon her hand, and Romeo adoringly wishing he were a glove on her hand so he could touch her cheek.
Romeo’s ‘But, soft! what light through yonder window breaks?’ speech retains some of Romeo’s love-struck hyperbole that we saw from him in Act I, but he is about to talk to Juliet again, alone at her window, and their mutual admiration will deepen as they resolve to be together.