How does this book help to explain the distrust that African Americans have with medicine and health care?
I'm glad that you wrote "help to explain," rather than "how does this book explain." There isn't going to be any one single cause of the distrust. Also, there are plenty of other people within every ethnic group that distrust medicine and health care. Entire religions exhibit that behavior as well. Christian Scientists, for example, are very outspoken about not using drugs and medicine.
As for the book, it highlights how the scientific and medical community took advantage of Lacks's cells. Her cells were the first to be successfully grown in lab cultures. They are still growing and reproducing to this day and are known as HeLa cells. The devious part of the entire situation is that the cells were harvested from Lacks without her knowledge. Once it was discovered that the cells were viable for lab growth and research, the cells were commercialized and sold to labs around the world. None of that money and profits ever made its way into the hands of Henrietta Lacks or her family.
What the book does is shed a very public light on a medical and research event in which the scientific community did not follow basic ethical rules. They knowingly took advantage of a patient and family in the pursuit of research. Lacks was an African American, so it makes sense that the African American community would be especially offended and distrustful of the medical community.