The terms "rising action" and "resolution" and "conflict" are normally used to analyze the plots of narrative works. Although Langston Hughes' "Mother to Son" is a relatively short poem, it does contain enough of a narrative to analyze using these terms.
The poem is about a mother who has risen above above her difficult circumstances to create a better life for her son. Hughes uses a "stair" metaphor to describe her ascent from the bottom, using images like "tacks," "boards torn up," and "goin' in the dark" to express how difficult her journey has been. These images help create the rising action of the poem/story--her journey up the metaphorical staircase. She is probably talking about rising up from a life of poverty and victimization.
In the resolution, the mother warns her son, "don't you fall now--/for I'se still goin' honey." This line expresses the idea that the mother's journey up from the bottom has become about her son--she must communicate the need for him to keep her progress going. It also implies that it is possible to lose the ground that she has worked so hard to win.
The conflict in the poem is between the mother and the son. Her warning in the resolution shows that she has reason to fear that her son might not continue up the stair, that he might "find it's kinder hard" and just "set down on the steps." After her hard life, this is something the mother does not want to happen.