Playing the Race Card

What is playing the race card exactly? Check out this post from Danielle Belton's The Black Snob for a hilarious parody. Here is an excerpt:

Mitt Romney raises his hand.

Romney: Um ... Your excellencies or ma'ams or sirs or brothers, sisters, people ... um ... what on earth are we talking about?

Al Sharpton shoves Romney a little.

Sharpton: They're talking about The Race Card, fool.

Romney: Wait? There's an actual race card? Like ... really? I thought that was just something us white people said when we wanted to belittle your problems. No offense. My dad marched with Martin Luther King ... in spirit.