Onomatopoeia is a language device in which a writer uses words which not only describe a sound, but also vaguely replicate that sound when said aloud. Writers often use onomatopoeia to create a vivid sense of place; a poem which uses onomatopoeia will sound a little like the scene being described simply because of the aural imagery created. In this poem, Langston Hughes uses subtle but effective onomatopoeia in his description of the stair the mother is describing to her son. Think about the word "splinters," for example—when we say this word, we can hear the sharp snap of wood as it breaks in the hard "t," while the "spl" sound suggests splitting. The word "splinter" sounds like the noise wood makes when it splinters, and we can imagine the sense of the mother's life splintering unexpectedly like this. The stair, of course, is a metaphor for her journey, and just as splinters arise out of nowhere and cause pain, so has that pain leapt out at the mother during her life.
Assonance is a language device in which the same or similar vowel sounds are repeated across several words. Assonance can lend cohesion to a poem's structure, particularly where there is no rhyme scheme, and can also add emphasis. The phrase "don't you set down," for example, has assonance on "don't" and "down" and emphasizes the mother's message: that even when life is hard, we cannot just stop.