Usually, I interpret it as people being seen for who they are--especially in terms of positive attributes--rather than being dragged down by negative racial stereotypes.
But it cuts another way, too.
When someone who is white commits a heinous act, I--as a white person--feel the pain the way humanity feels the pain, but I am not expected to feel the guilt or the shame or to bear any responsibility because I share the perpetrator's skin color. In fact, I do not have to worry that his or her actions will reflect on me in any way.
That is my privilege.
This is my dream: That one day all people who commit heinous acts will be judged by the content of their character and not be used to judge others who share the color of their skin.