Racism is a problem in America, and one of the ways that it manifests itself is through white privilege. Some white people, especially those who have never really had a lot of conversations about race, think that even acknowledging a person's race makes them racist, or that it's better not to talk about it and the state of race relations in our country would be better if we just left it alone. These ideas lead to a false ideology of "colorblindness" by which white people refuse to acknowledge the races of minorities when they interact with them, insisting that they treat everyone the same regardless of their race. But despite its good intentions and surface-level conciliatory tone, colorblindness is just a dressed-up form of white privilege.
For starters, colorblindness treats white as the norm and everything else as a deviation from it, in the same way that self-deprecating jokes about being "just white" do. I've heard several well-meaning white people, when asked about their ethnicity, respond by saying "Oh, I'm just normal. I'm white." Being non-white is not abnormal. White people are not the most populous race in existence by a long shot. Human beings don't come standard with European heritages.
In addition to treating anything that isn't white as abnormal, pretending not to notice a person's race means you're denying a part of that person's identity that is potentially very important to them. Imagine if one of your friends who is a minority said, "Oh don't worry, I don't even think of you as a white person." Insisting that someone's race is not on your radar screen makes it seem as if their race is a negative trait that they've somehow managed to overcome. Not cool.
And the final, possibly biggest, reason why colorblindness is just another form of racism: to be able to claim that you are "colorblind" about other people is in itself coming from a place of privilege. As white people we have the luxury of deciding whether we want to engage the topics of diversity, race relations, and systemic oppression. Minorities in America don't get that choice. They are treated differently because of their race; that is their reality, and they have to live in it whether they like it or not. Minorities don't get to decide the vast majority of the time that their race is a non-issue, because they can't afford to pretend that people don't notice. By pretending that you don't notice, you're just taking advantage of a way that American society makes your live easier because you're white at the expense of someone else. That's white privilege.