What is Race?

We attempted to answer this question in class, but I've never really thought of the answer. It just never entered my mind. I thought it was some vague definition, with ethnicity, skin color, heritage, cultural identity, and physical features of some sort included. It seems really complicated; or not. Maybe it's something that we as a society makes up for the sake of labels and stereotypes. I'm torn.
This morning, our teachers also asked how many races there were out there. Now that's impossible to answer. There must be hundreds; thousands. I remember there being a really controversial case on the Evanston School Board about Hecky (a black man who runs a really great BBQ restaurant on Green Bay) and how during a discussion about issues within the school about being black, and what it means to be "truly" black, he said "We're just a bunch of mutts anyhow. I don't know what the big deal is." He was fired afterwards, but I'm not sure why. I completely agree with him. People have not been breeding with just their own race since the dawn of man-kind. No one is "completely white"or "completely black". There are millions of variations of people, skin color, and ethnicity in the world.
Today, My friend ironically wore a "stereotypes make everything easier" shirt in school. I guess the fact that there are millions of variations on race just complicates things :)