"Privilege" is a current buzzword on the Left.
"Check your privilege" is Left-speak for "shut up." It implies that if you're white or male or otherwise "privileged," in the rather narrow sense in which the Left uses the term, your viewpoint is skewed and/or invalid. Of course, in the Leftist way of looking at things, if you simply disagree with the politically correct party line for any reason whatsoever, then your viewpoint is skewed and/or invalid.
Only that which agrees with The Narrative may licitly be spoken or heard. It's simply a function of the essentially totalitarian nature of "progressivism."
But not if you're an "unprivileged" person who might not be white or male or straight, but just far more powerful and influential and set apart for preferential treatment precisely because you're not white or male or straight.
Or otherwise "privileged." Which a very large percentage of "progressives" turn out to be- far more so, in fact, than whiteness or maleness or heterosexuality accounts for.