It's a theory which teaches that white males, who are the ones in power, have systematically discriminated against and created disadvantages for everyone else in areas of education, employment, housing and so forth. And therefore white males are responsible for poor living conditions, poor employment, unemployment, crime, incarceration and so forth that everyone else experiences.
You're missing the key element: History. Historically white males have created systems that primarily have benefited other white males. Those systems therefore have historically made it more difficult for people of color, and women in general, to advance themselves the way white men have historically been able to advance themselves. Wealth is also a major factor--the rich have created and run systems that primarily favor and benefit themselves, at the expense of the poor.
Because these historical forces have been at work, many of our systems of government, education, economics, etc are still plagued by that history.
Yes, I--as a white male--have benefited from such systems. I've never had to face discrimination on the basis of the color of my skin. I've never been discriminated against because of my sexual reproductive organs. I've never been discriminated against on the basis of my sexuality. I've always been one of the "normals". I was born into a world that was designed to make me feel far more comfortable in it than those who are not like me.
That doesn't lead me to hate the color of my skin. I have pride in my Irish and German heritage. I celebrate it. So clearly recognizing my white privilege doesn't make me feel guilty for being white, or make me hate my ethnic and "racial" heritage. It just makes me aware of the ways I've benefited and, more importantly, that others have not benefited, and in fact many others have faced a lifetime of setbacks, obstacles, and roadblocks that are entirely outside of their control.
Do some people do a better job at explaining this than others? Well of course. But most people that I've seen who are educated and informed on these topics do a pretty good job of explaining it and making it quite easy to understand.
At the end of the day, however, this isn't anything that we haven't all, on some level, already known our entire lives. I've always known that I've benefited from being white, nobody actually had to tell me that. Even in my extremely conservative elementary school history classes I could read and learn about colonialism, the treatment of indigenous peoples, the Atlantic slave trade, the institution of slavery, Jim Crow, and the Civil Rights Movement. I could see how the one black kid in my class was treated differently than the rest of us with my own eyes. He wasn't bullied, or called slurs, but he was treated different. He was treated different than how I and all the other white kids were treated. I could see how uncomfortable he looked. And I was only 10 years old.
So explaining in greater detail things which, frankly, I already knew my whole life--but learning just how deep those problems run--has not made me feel bad about my DNA. But it has made me aware of just how deep the problems go, and just how deeply and desperately needed it is to address these things.
-CryptoLutheran