What do you think is Langston Hughes' purpose in writing the poem "Mother To Son"?

In “Mother to Son,” Langston Hughes assumes the persona of a mother who is having a heart-to-heart conversation with her son. His purpose is to show that the strongest people in life persevere through difficulties.
In this poem, a mother uses several metaphors to convey the ways she has seen adversity. Her life has been filled with “tacks” and “splinters.” There have been times when she had seen the foundation of her life stripped to its core, lacking the comforts of “carpet”—simply bare.
Yet, she notes that she has never given up. She has climbed the metaphorical stairs of her life by reaching one “landing” at a time, barely catching her breath before beginning the next climb. This mother has struggled through the depths of despair and grief, “sometimes goin’ in the dark/Where there ain’t been no light.”
But the tone shifts at the end to align with the purpose. This mother wants her son (and the reader) to be encouraged by her experience. Her struggles have not defined her. Her experience has led to this wisdom:

Don’t you set down on the steps
’Cause you finds it’s kinder hard.
Don’t you fall now—

Because she has made it in spite of her difficulties, there is hope for her son and for anyone else who doesn’t find life to be made of a “crystal stair.”

The purpose of the Langston Hughes poem "Mother to Son" is to illustrate, through narrative, the difficulties that previous generations of black people have endured, sometimes as a sacrifice to ensure a better future for the next generation.
It is significant that Hughes chooses to make the narrator of the poem a black woman. This device shifts the reader away from the convention of a father passing down life's lessons to a son, while also centralizing the often neglected struggles of black women in a racist system.
In the first line, the mother makes it clear that, though she is a woman, she has never been placed on a pedestal: "Life for me ain't been no crystal stair." She narrates a story of struggle, characterized by the "splinters," "tacks," and other obstructions that have hurt her as she labored on. However, she remained resilient:

But all the time
I’se been a-climbin’ on,
And reachin’ landin’s,
And turnin’ corners,
And sometimes goin’ in the dark
Where there ain’t been no light.

The mother's purpose in telling her son this is to motivate him to endure, even when life becomes unbearably difficult:

Don’t you set down on the steps
’Cause you finds it’s kinder hard.
Don’t you fall now—
For I’se still goin’, honey,
I’se still climbin’,
And life for me ain’t been no crystal stair.
https://www.poetryfoundation.org/poems/47559/mother-to-son