In I Know Why the Caged Bird Sings, what problem does Marguerite have in the story that Mrs. Flowers talks to her about?

Well, the root problem is the abuse that Marguerite
suffered when she was living with her mother at the hands of her step-father. As Chapter
14 makes clear, the impact that this horrendous incident has on Marguerite is to make
her hate herself which in turn makes her hate her life and robs her of any joy that she
might have:

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Sounds came to me dully, as if people were
speaking through their handkerchiefs or with their hands over their mouths. Colours
weren't true either, but rather a vague assortment of shaded pastels that indicated not
so much colour as faded
familiarities.

Mrs. Flowers
speaks to Marguerite directly about the way that she won't speak in class or to anyone
else. Marguerite seems to have closed in on herself like a flower who refuses to bud,
and Mrs. Flowers directly addresses this issue,
saying:

Now no
one is oging to make you talk--possibly no one can. But bear in mind, language is man's
way of communicating with his fellow man and it is language alone that separates him
from the lower animals.

Thus
it is that Mrs. Flowers challenges Marguerite's perception of herself and of others, and
gradually fills her once again with self-respect and self-love through the simple
process of spending time with Marguerite and letting her know that she is valued and
esteemed.