We real cool. We Left school. (lines 1-2)
The boys all speak as one, like a chorus. Also, the first line validates the second. As in, we might know they "left school" because of the ungrammatical phrase "we real cool." However, there's no reason people should have to speak with perfect grammar in poetry – or in the real world. "We real cool" suggests jazz rhythms, and it brings to mind a different set of connotations from saying, for example, "We are really cool." Finally, "We real cool" is the only sentence in the poem without a verb in it.
Sing sin. We Thin gin. We (lines 5-6)
Just look at how this stanza appears on the page. If you removed the period in the middle of each line, it would look like a normal sentence with the subject at the end instead of the beginning. You might compare this to Yoda grammar, where the verb comes at the end: "Welcome, you are." Also, the words "sing," "sin," "thin," and "gin" look really similar. They make the stanza look like the result of a very productive game of Boggle. How does the simplicity of the rhymes, coupled with the use of alliteration, complicate the speaker's attempt to convey meaning? Is sound more important than sense (i.e., the meaning of the words)?
We Jazz June. (lines 6-7)
In this sentence, "Jazz" functions as a verb. Is Brooks just making words up, or does this sentence produce meaning? The pool players thumb their noses at society throughout the poem, so maybe their use of ungrammatical expressions is an example of how they are mocking grammatically correct society.