White privilege has to do with implicit bias and how you are perceived by others. IN GENERAL (because of course there are always outlying examples) a white person can walk down the street without someone assuming they are a thug, or a criminal, or uneducated, or a danger or a threat.
I've said this before I'll say it again. People profile others based on observation. Young black males account for about 50% of violent crime in America despite being a small percentage of the nation. Does that mean all black males are criminals? Of course not, but when people see the same type of folks in the news and media as responsible for large amount of crimes, this has an effect.
And this is not really about race. A 70 year old black man does not invoke that fear, neither does a middle age black woman, nor a teenager black girl.
This is not just the responsibility of the larger population to force their minds not to have this fear, though I would argue everyone needs to be given a chance to show what their worth. But the people being profiled also have some responsibility to help change stereotypes.
When italians came to this country they were victims of persecution and stereotyping.They had a really tough time being accepted and being integrated. What happened? Did they protest and demand that society change their mind? Well, no. They simply began gaining the trust and admiration from others to the point where over the years they were fully accepted.