The poem repeats many key words and phrases, both as a way of highlighting its main themes and as a way of loosely structuring its free verse.
Take the word "dream," for example. It appears seven times in the poem's 33 lines (including once in the plural: "dreams," line 33). In all but one of those instances, the poem further emphasizes it by placing it at the end of a line. ("Dream"/"dreams" ends so many lines that it's almost a refrain!) In five instances, it occurs as part of the phrase "my dream," and in two instances, as part of the phrase "the light of my dream."
This constant repetition conveys how important—in fact, essential—the "dream" is to the speaker's imagination. It's something deeply personal, a guiding "light" in their lives, even as the "wall" of racism blocks them from attaining it. This "wall" is itself mentioned four times; so is the fact that it "rose" up, and the oppressive "shadow" it casts. These repetitions illustrate the maddening persistence of the racial barrier.
Meanwhile, "light"/"lights" appears three times, indicating that the gleam of hope hasn't completely vanished from the speaker's life. (Since shadows are dark and light is, well, light, there's also some complex racial symbolism at play here. In breaking down the wall, the speaker seems to want to erase the light/dark distinction entirely, or end racial divisions altogether.)
Some repeated words/phrases fall at the beginnings of successive lines and/or sentences, creating anaphora. Examples include "Rose" in lines 11 and 15, "Only the" in lines 22 and 23, "My" in lines 24 and 25, "To" in lines 29 and 30, and "Into a thousand" in lines 31 and 32. Other repeated words/phrases fall at the ends of lines: "dream"/"dreams" (lines 2, 6, 10, 14, 27, and 32), "me" (lines 4, 20, and 21), "sun" (lines 5, 31, and 33), "slowly" (lines 8, 9, and 11), "wall" (lines 16, 22, and 26), "shadow" (lines 17, 19, 23, and 30), and "hands" (lines 24 and 25).
Some of these repetitions emphasize key themes (e.g., the "wall" of oppression) or convey emotion (such as the excitement of "Into a thousand lights of sun, / Into a thousand whirling dreams / Of sun!"). More broadly, by starting and ending so many lines with identical phrases, the poet adds a dash of structure to an otherwise free-form poem. There's no set meter, rhyme scheme, or stanza form here, but the poem does keep circling back to the same words and ideas.