It is from this article. It is in the heading.
African women on the shame of hair loss.
Does it just mean they feel shame?
I think it is missing a comma. It is the title of the article, maybe they couldn't have a comma in a title?
I think it should be African women, on the shame of hair loss.
I think the parts before and after the comma should basically be interpreted like two separate sentences. The article is about African women. The article is about the shame caused by hair loss.
Another interpretation may be "African women talking on the topic of the shame of hair loss". Yes, I think that's a better explanation.
Rewrite it with a verb:
African women talk about the shame of hair loss.
on is often used as a synonym for talk about or gives an opinion on something, especially in headlines or as the title for opinion columns.