Amnesty International is a human rights organization that was founded in London. Its work centers on the rights of prisoners of conscience, men and women whose governments have imprisoned them for their beliefs, ethnic origins, or religions.

In this writing, what does "Its work centers on the rights of prisoners of conscience" mean?

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"Its work centers on" means that Amnesty International primarily works on the following goals, which the sentence then goes on to explain.
The phrase "the rights of prisoners of conscience" refers to people who are in prison not for committing crimes like stealing or murdering, but for simply having a belief that is different than the government's, or even just for being a certain kind of person that the government does not like. So, Amnesty International believes that people have rights which are essential to being a human being. Governments can, and sometimes do, deny them those rights and put people in prison because what they believe or do, or who they are, is something other than what the government likes.