Let's look at the third verse as an example:
Lights is blinding, girls need blinders
So they can step out of bounds quick, the sidelines is,
Lined with casualties, who sip to life casually
Then gradually become worse, don't bite the apple Eve
We can split up the first four lines into two couplets, that is, pairs. Looking at these lyrics printed on the page, there might seem to be some rhyming problems, though. "Blinders" is made to rhyme with "-lines is," and "casually" is supposed to rhyme with "apple Eve." And there is also the inner rhyme of "casualties" with "casually." Those rhymes don't look beautiful; maybe they don't even look like rhymes. But don't forget that hip-hop is primarily an aural art form. The lines sound a lot better than they look.
In part this is due to Jay-Z's use of African American Vernacular English. In this English dialect, rooted in the nation's black communities – though in cities and in the entertainment industry it is becoming more commonly associated with hip-hop culture, regardless of race; see: Justin Timberlake – it is common to deemphasize the last sound of a word, or remove it completely, while stressing the initial syllable. ("Door" might become "doh," for example, or the second-syllable emphasis in a word like "police" might be moved to the first syllable.) So for "blinders" and "-lines is" it doesn't matter so much that "blinders" ends with an "-ers" sound and "is" ends with a "z" sound. These last syllables aren't emphasized. What's more important to the ear is the similarity of the "blin-" in "blinders" and the "line" in "-lines is." In poetics this is called feminine rhyme, the rhyming of the last two syllables with an often-unstressed final syllable.
But it gets better. Rhyming couplets isn't enough. Rappers have to string these rhymes together more rapidly than once every ten-or-so syllables. The next few lines of "Empire State of Mind" demonstrate this:
Caught up in the in-crowd, now you're in style
End of the winter gets cold, en vogue, with your skin out
City of sin, it's a pity on the wind
Good girls gone bad, the city's filled with them
One of our more technically skilled rappers, Jay-Z uses what is called inner rhyme countless times in this song – something other rapid-flow MCs like Eminem are known for as well. This section of "Empire State of Mind," no doubt one of the best raps in the song, is filled with inner rhyme. How many instances of inner rhyme can you see just in the first two lines?
In the first line "in the," "in-crowd," and "in style" are all feminine rhymes, with the "in"s rhyming. We get more of this in the next line. "End of" (which you hear as "in dove"), "en vogue," and the "-in out" of "skin out" all continue Jay-Z's march of feminine rhymes. It's a beautiful and highly skilled rhyming scheme.
This is not, of course, to say that this is original or especially innovative, lest we forget the centuries upon centuries in which poets like Alexander Pope demonstrated expert use of all rhyming techniques. And an earlier musical example though might be found in Bob Dylan's "Subterranean Homesick Blues." In other words, Jay-Z's working in a rich poetic (and musical) tradition here.
(PS: yeah that's right, we just compared Jay-Z to Alexander Pope and Bob Dylan. Deal with it.)
You might be thinking that a few of these rhymes are kind of weak. And maybe some are; "casually" and "apple Eve" don't rhyme too well. But Jay-Z makes sure he gets some powerful, definitive sounding, lines in at the end of each verse.
Look at the last four lines here:
Came here for school, graduated to the high life
Ball players, rap stars, addicted to the limelight
MDMA got you feelin' like a champion
The city never sleeps, better slip you an Ambien
These lines aren't overflowing with rhymes, but the two rhymes, "high life" with "limelight" and, better, "champion" and "ambien," are great. Why are they so strong, though? In the previous section, Jay-Z's feminine rhymes often didn't rhyme the final syllable. But here, "champion" and "ambien" clearly, completely rhyme. Often times in poetry, clear, straight rhymes like these have the effect of halting verses. Have you ever heard a limerick read straight through?
Here Jay-Z doesn't need to show off how good he is at rhyming. He has to close off the verse and transition into Alicia Keys' soaring chorus! So these definitive-sounding rhymes wrap up Jay-Z's verse while still declaring his skill.