A sensitivity reader is someone who has a writing or editing background (or is simply an avid reader) with extensive personal experiences that they use to draw upon when they review projects submitted to them for misrepresentations, bias, racism, or unintentional stereotypes.
Sensitivity readers are not regular editors or censors. They do not proof, look for holes in stories, or rewrite or delete content. In fact, all projects given to sensitivity readers are given voluntarily.
Sensitivity readers simply read for what they consider to be offensive content, misrepresentation, or stereotypes, and point it out. The author of the content chooses whether to use their suggestions or not. A sensitivity reader is also someone who specializes in a specific niche (African-American, Muslim, physically challenged, LGBTQ, Little People, the obese, etc.) and are part of the specific marginalized community that the author is writing about. The sensitivity reader thoroughly reads over the material for bias, stereotypes, offensiveness, lack of understanding, etc., and creates a report for the client outlining their thoughts, why they feel something may be a problem, and offering possible solutions.
If you are writing about more than one marginalized group, and you are not part of those groups, then you would do well to hire sensitivity readers who specialize in each group.