When a non-black person criticizes a black person, he may feel there is a need to disprove the influence of racism on his opinions. So, he proves he's not racist by citing another black person who also criticizes the first black person. Stephen Colbert coined the term on September 24th, 2009.
Blackwash can be used as either a noun or a verb.
Mr. White: I've been saying for a long time that Mr. Black's policies are terrible. An African-American writer from the New York Times criticized him too.
Mr. Black: Don't blackwash me. Why do you need to point out that the writer is black?