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.

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.