Epic, Passionate, Poetic
Right from the Prologue we know Shakespeare wants to make this play a big deal. Check out how epic his language is, right from the beginning:
Two households, both alike in dignity
(In fair Verona, where we lay our scene),
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
From forth the fatal loins of these two foes
A pair of star-crossed lovers take their life; (Prologue.1-6)
Obviously, this isn't going to be a romantic comedy, not with mighty words like "ancient grudge," "civil blood," "fatal loins," and "star-crossed lovers." Melodramatic? Sure. But Shakespeare makes it work, because the plot actually does live up to the hype.
Besides choosing epic-sounding words, Shakespeare pens a slew of passionate exchanges. In addition to Romeo and Juliet's romantic moments, lots of other characters get passionate dialogue, like Mercutio's repetition of "A plague o' both your houses!" (3.1.94), and Friar Laurence's "Ah, what an unkind hour / Is guilty of this lamentable chance!" (5.3.150-151). Again, it might seem melodramatic—but it's totally appropriate for the play.
Blank Verse
Well, you didn't think you were going to get away without some poetry, did you? Expect for exchanges between servants and some bawdy jokes, Romeo and Juliet is written in blank verse, which is a less-fancy way of saying "unrhymed iambic pentameter." "Unrhymed" is pretty straightforward, but let's break down that iambic pentameter stuff.
Starting with the first word: "Penta-" means five, so we know we've got five of whatever a "meter" is. A meter is a group of two syllables, or "feet." The two feet are either stressed or unstressed, in some sort of pattern, which gives the line that certain rhythm that makes the line sound "poetic." Put it all together, and all of Romeo and Juliet's lines will have ten feet, or ten syllables.
Now for the "iambic" part. An "iamb" is a foot, the basic unit of meter. It's a stress pattern—actually, the most popular stress pattern in English—composed of an unstressed syllable followed by a stressed syllable. Think, "negLECT," "oBEY," "toNIGHT," or "misTAKE."
The easiest way to explain this is to just sound it out. Let's look one of the lines from the Prologue:
in FAIR | VerON | a WHERE | we LAY | our SCENE
or
where CIV | il HANDS | make CIV | il BLOOD | unCLEAN
Notice how we skipped a line there? That's because not every single line is perfect iambic pentameter. Line after line of perfect meter ends up sounding more like a nursery rhyme than poetry, so poets (and playwrights) will play with the meter to emphasize certain words. Let's skip back to one of the non-perfect lines in the Prologue:
From ancient grudge break to new mutiny,
From AN | cient GRUDGE | BREAK to | NEW MUT | ti NY
See how the meter gets all wacky in the middle there? By stressing the first syllable of the third foot, Shakespeare calls attention to the violence of the "break"—the syllable breaks out of the meter, just like the violence breaks out in the city. Pretty cool.