"Good night, good night. Parting is such sweet sorrow, That I shall say good night till it be morrow."
Juliet does not want Romeo to go, but the sun is coming up and he must leave or their love will be exposed. She says that she will keep saying goodbye for so long that tonight will become tomorrow. She is saying that she cannot stand to see him leave because he is the love of her life and she never wants him to be away from her side.
"Thus with a kiss I die."
Romeo believes Juliet is dead and he cannot live without her. So, he drinks the poison given to him in order that he might join her in death. He kisses her as his last living act.
"Yea, noise! Then I'll be brief. Oh, happy dagger, this is thy sheath; there rust and let me die."
Juliet sees that Romeo has killed himself upon seeing her body in the tomb. At this discovery, she decides she cannot live any longer. With people fast approaching who may try to stop her, she takes the knife and says that her body will become its sheath. She will stab herself and the blade will stay there until it rusts long after her death.
“What's in a name? That which we call a rose
By any other name would smell as sweet.”
Here, Juliet ponders the nature of identities and the arbitrariness of the names of things. She's crestfallen that the boy she fell for at her family's party is the son of Montague, her family's only enemy. She posits that if a rose can smell exactly the same way even when it's not called a "rose," then she should be able to love Romeo just the same even if he's called something else. In essence, she's criticizing the power of all names, including those that govern her family's feud.
“See how she leans her cheek upon her hand.
O, that I were a glove upon that hand
That I might touch that cheek!”
At this point in the film, Romeo's love for Juliet is brand new and knows hardly anything about her. Watching Juliet touching her own face, Romeo wishes to be a glove on her hand so that he can touch her, too, as even the idea of that is exciting and unfamiliar, and standing below her balcony, having as of yet not made himself known, he feels too distant to do it.
"But soft! What light through yonder window breaks?...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."
In Roman mythology, Diana was the goddess of the moon, as well as virginity and childbearing. Watching Juliet lit by the light coming from her window, Romeo is suggesting that Juliet is a servant to the moon, and therefore Diana, because she is a virgin, but that the moon is jealous of Juliet because she is more beautiful.
"Then I defy you, stars!"
As touched upon at many points in this guide, Shakespeare is suggesting that the stars are tied to fate, that they lay out people's destinies. In hearing of Juliet's death and deciding to take his own life, Romeo believes he is actively going against what the stars want: presumably, for him to stay alive.
"My only love sprung from my only hate!"
The greatest irony of Romeo and Juliet is that the two titular characters each have a single person in their life with whom they are forbidden to fall in love: the offspring of their enemy family. And yet, of course, it is that person for whom they each fall. In this moment, Juliet is aghast to discover that Romeo's last name is Montague, and that the only boy she truly loves was borne of the only family she is supposed to despise.
"The fearful passage of their death-marked love,
And the continuance of their parents' rage,
Which, but their children’s end, naught could remove..."
This story does not beat around the bush when it comes to foreshadowing: you are about to watch a film in which Romeo and Juliet die to end their families' feud, and Shakespeare wants you to know it from the get-go. As Romeo and Juliet is, through and through, a commentary on the dangers of impulsivity, rampant passion and unchecked emotions, it's important to establish at the story's opening that this is not going to end well and you should remember that as you weigh the characters' decisions throughout the narrative.
"From ancient grudge break to new mutiny, Where civil blood makes civil hands unclean."
Another example of foreshadowing, this line is a crucial nod to the story's turning point, in which Tybalt accidentally kills Mercutio and then Romeo seeks revenge by killing Tybalt. It's an acknowledgment that the families' feud corrupts everyone involved, such that no one will be spared its unclean influence by the time the tale is through.