Couplets with Internal Rhyme
Apart from its subtitle ("THE POOL PLAYERS/SEVEN AT THE GOLDEN SHOVEL"), "We Real Cool" has four stanzas, each of which is a two-line couplet. Every word in the poem has only one syllable.
While many traditional couplets in poetry have a rhyme at the end of the line, this poem takes rhyming to a new level: the couplets rhyme in the middle. Thus, "cool/school" in the first stanza, and "late/straight" in the second. But the pause after each rhyme word effectively makes it sound like the end of the line. It's almost as if each line ends on a rhyme word, and "We" is tacked on as a grace note. (In musical terminology, a grace note is a short note that gets squeezed in before a beat.)
The poem has a regular meter, with three beats and a pause, but these three beats can be pronounced in different ways. You could say, "We real cool," or "We real cool," or "We real cool," or, even, "We real cool." In the recording we listened to (hear it on Poets.org), Brooks lay the most emphasis on the second two beats: "We strike straight."