People and Colour? What does it mean?

Who is Black? Who is White?
What is meant by saying that a person is Black or White?
Is it skin colour or is it something else?

Is President Obama Black? To me, he is a lot fairer-skinned than a lot of "white" folks, especially those with a strong tan.
Is Black a colour or a race or what?

I recall a statement from the 60's: If you are not white, you are black. There is no room for those with a colour of brown, yellow, red, etc., some of whom have experienced a fair measure of discrimination, covertly or overtly. If one of your parents is white and the other is black or some other colour, you are automatically black: this seems to be the case with President Obama and some of the most beautiful women in the world.

When I attended university in Canada in the 60's and 70's, I travelled by bus from the university campus to where I lived. I recall very vividly, an incident on such a trip. I boarded the bus early and got a seat. Another student, Joe, from Nigeria, whom I knew, also boarded early and got a seat in front of me. As with most buses, each seat could accommodate two persons. More students boarded the bus and soon there was standing room only, except for the seat next to Joe. A white female student decided to stand next to the seat in which Joe was sitting, even though there was a space next to him where she could sit. Joe was a tall, well-built, dark-skinned person who was always impeccably dressed in his full suit with jacket, tie, and overcoat.

Joe was enraged at this incident. He took his books, which he was keeping on his lap, and slammed them down on the vacant seat. He turned around to face me and said "Black and White are like two parallel lines that will never meet". He also removed a sheet of plain white writing paper from his folder, showed it to me, and said "This is White", inferring that people who call themselves white should really have a colour similar to the sheet of paper.

So once again, I am asking:

Who is Black? Who is White?