Should I understand that they use the labor of prisoners - a large proportion of them black
men - to make profits?

It wouldn't surprise me, although I doubt there's any direct proof of that at the time being.

Since you're interested in the topic, though, here's an interesting article:

http://www.motherjones.com/politics/2016/09/10-things-cca-investigation

Sorry.....Corrections Corporation of America (Now also know as CoreCivic.)

Yes, indeed, there's a huge prison population here in America - more than anywhere else in the world. This is closely tied to the imbalanced sentencing of minorities to whites and the prisons for profit that encourage such sentencing, and in my mind is a huge violation of human rights.

"The United States is experiencing a major human tragedy. We have more people in jail than any other country on earth, including Communist China, an authoritarian country four times our size. The U.S. has less than five percent of the world’s population, yet we incarcerate about a quarter of its prisoners — some 2.2 million people."
Bernie Sanders

"CCA has made profits from, and at times contributed to, the expansion of tough-on-crime and anti-immigrant policies that have driven prison expansion. Now a multi-billion dollar corporation, CCA manages more than 65 correctional and detention facilities with a capacity of more than 90,000 beds in 19 states and the District of Columbia. The company’s revenue in 2012 exceeded more than $1.7 billion."
from "Just Like Selling Hamburgers," by Matt Straub (found in Forbes online)

Human rights, for example, is a topic that's going to haunt
China for a long time, but Germany's terrible reputation on that subject has long
disappeared.

Interesting observation.
I would add that it seems that much of the German population is aware of their tragic brutal history. Unfortunately, few U.S. citizens are aware of the long imperialist history of U.S. military invasions and covert destabilization of democratically elected government, a list too long to post. Keeping the U.S. population in the dark with delusions of "American Exceptionalism" continues and is remarkably successful. A 3rd world educational system, a corporate media, and a political system of capital cronyism empower this deceit.

I've been in China over a decade, and I am not truly aware of what percentage of the Chinese people are 'haunted' by China's own human rights shortcomings. It seems to me that most are satisfied to pursue the new car, new house, and enormous flat screen TV that was the sum of the U.S. populace's concerns during my father's generation in the years from 1945 thru 1965. Future generation of Chinese, once their material needs are taken for granted, will likely pose problems for the Communist party, as my peers did for the U.S. in the late 60s and 70s.

I'm quite sure that the Chinese leaders are aware of this, which explains their diligent attempts to control social media and college campuses.