The quote is taken from act II, scene II of the play, after Romeo and Juliet have already met at the Capulets’ party. Romeo is captivated by Juliet’s beauty and believes that he is in love with her. In this passage, he ascribes celestial, angelic attributes to her, meaning that she is so glorious that she transcends above all earthly human traits. Juliet is equally besotted by Romeo and cannot sleep after the party has ended.

She is on her balcony above Romeo, who is below in the Capulet’s orchard. Juliet is sighing and speaking to herself. Romeo loves the sound of her voice and wants to hear her speak again. He says to himself,

Oh speak again, bright angel! For thou art

As glorious to this night, being o'er my head,

As is a winged messenger of heaven.

The comparison of Juliet to a celestial creature far and above anything as mundane as a human being is clear in the quote. Romeo uses words such as “bright” almost as if Juliet herself were a star, “angel!” imbuing Juliet with angelic or super-worldly traits and “glorious,” as a reference to the glory of G-d’s heaven. As a biblical term, the use of the word glory was intended to convey splendor, power and greatness. By referring to Juliet as glorious, Romeo is therefore both extolling her as a person above him and referencing the aspirational aspect of his feelings for her.

Juliet is figuratively and literally above Romeo, just as the stars above are. He refers to her as “being o'er my head” and compares her to “a winged messenger of heaven," which is another reference to Juliet as an angel, too beautiful and good to be of this earthly realm. The quote means that Romeo wants to love Juliet in an emotional, physical, and spiritual sense.

The above quotation comes from the famous balcony scene in Romeo and Juliet. In this scene, Romeo repeatedly uses lush, romantic language to describe his beloved Juliet and the powerful feelings he has for her.

In this particular case, he refers to Juliet as an angel. But not just any old angel; a “bright angel” who looks particularly glorious tonight. Juliet has only spoken two words so far in this scene—“Ay, me!” or “Oh, my!”—but Romeo is already so captivated by her that he wants to hear her speak again:

She speaks,

O, speak again, bright angel! (II, ii, 25–26)

Everything about Juliet is so wonderful to Romeo: her looks, her voice, the way she comports herself on the balcony. The young man is utterly smitten, and he expresses his powerful feelings by using flowery language, describing Juliet as an angel, a winged messenger of heaven who shines brightly in the skies above him. In the words of the song, heaven must be missing an angel, and that angel is Juliet.

In case we didn't already know it, this is no ordinary love, no repeat of the boyish infatuation that Romeo developed for Rosaline. This is the real thing, a powerful, enduring bond of love that cannot be broken, not even by death—love which appears, like Juliet, to have come straight from heaven.

The quote,"O, speak again, bright angel!  for thou art as glorious to this night, being o'er my head, as is a winged messenger of heaven..." was spoken by Romeo in Act II, Scene 2, the famous balcony scene.  Juliet is saying that Romeo's name is her enemy and not his being. Romeo is hanging onto every word Juliet speaks.  He is comparing Juliet to Cupid the messenger and saying they are both welcome entities to him.  He feels both are sent from Heaven.

This line should read as follows:

She speaks.
O, speak again, bright angel! for you are
As glorious to this night, that is over my head,
As is a wingéd messenger of heaven
To the white, upturned, wondering eyes
Of mortals that fall back to gaze on him
When he crosses the slow moving clouds
And sails upon the heart of the wind.

Romeo has been watching Juliet from below the balcony when he hears her sigh. In this aside, he refers to her as a bright angel against a dark sky; he says that she is as wonderous to his eyes (gazing up at her against the darkness) as an angel sailing upon the heart of the wind would be to mortals. Like any other man looking upon a heavenly being (such as Juliet), Romeo feels awed, and would "fall back" to gaze upon her. This is consistent with Romeo's character, for he is frequently awed by the women he is infatuated with, and tends to look upon them not as real humans but as heavenly beings (Rosaline is like the moon, Juliet, an angel and the sun). Against the darkness that covers him (is over his head), Juliet appears like a bright light. She is that, too. Prior to meeting her, darkness was not just over his head, it was in his heart. Now, he is separated from the dark sky by his vision of Juliet.

These words are spoken by Romeo after he's met and fallen in love with Juliet at the Capulet party. After the party, Romeo ditches his friends and climbs over the wall of the Capulet orchard. Juliet comes out on the balcony and is speaking her thoughts and feelings about meeting Romeo that night (soliloquy). As Juliet pauses, Romeo wants her to speak again, comparing her to an angel in heaven.

In these lines, Romeo is referring to Juliet. He is using a simile (a comparison using 'like' or 'as') to compare Juliet to an angel.

An angel, a "winged messenger of heaven", is as glorious to the night as Juliet is to Romeo. (A metaphor)

A lot of times line breaks in Shakespeare can be confusing. When you read, just read with the punctuation and do not stop at line breaks. That might help you understand a little easier.