What do the sun and moon symbolize in Romeo and Juliet?

Shakespeare plays with images of light and darkness throughout Romeo and Juliet; indeed, many of the scenes happen either late at night or early in the morning. In act 2, scene 2, however, Romeo provides some of the most famous lines in all of English literature:

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. (II.ii.44-47)

In these lines, Romeo compares Juliet to the sun. This is after the Capulet party, and Romeo is awaiting a glimpse of his beloved as he waits below her balcony. It is dark, late at night, and Romeo believes that Juliet's beauty is enough to transform the night into day, much like a sunrise.

It's also important to remember that Romeo has been through his own symbolic "night" recently over Rosaline's rejection. In fact, just before this party, Benvolio has to persuade Romeo to even attend, telling him to "Compare her face with some that I show,/ And I will make thee think thy swan a crow" (I.ii.87-88). It could also be argued that Rosaline is the darkness that has encapsulated Romeo's heart, and Juliet is the sun that breaks through that darkness with her beauty.

Romeo goes on to ask Juliet to appear at her window ("Arise, fair sun...") and "kill the envious moon." Here, the moon symbolizes the passions Romeo held before, whose light and beauty pale in comparison to the bright and beautiful Juliet. Romeo realizes that anything he considered love before beholding (and kissing) Juliet is inconsequential.

The lines that your question is asking about can be found in the beginning of Act 2, Scene 2. Romeo is in Capulet's orchard, and he is waiting for Juliet to come out on her balcony. When she finally does come out, Romeo compares Juliet to the sun rising in the east. As the sun (Juliet) rises, it (she) outshines the "envious moon." Romeo is saying that Juliet is so fair and lovely that she outshines any other girl that might have feelings for Romeo. The moon represents any of those other girls. The moon (another girl) is "envious," because it knows that Juliet is far brighter and more attractive than it (she) is. Scientifically speaking, the sun is definitely both brighter than the moon and more "attractive," in that its gravitational field is stronger. The sun creates its own light, and it is way more massive. More mass means more gravity. More gravity means a stronger attraction. I may not like Romeo, but his metaphor in this case is a good one.