Race is one of the most misunderstood words in the English language.
It literally refers to any genetically passed traits that are shared within a group. This can include skin-colour, but it also includes hair colour, freckles, even nationality. In other words, any shared genetic traits mean you share the same "race" as someone. As you can imagine, this makes the term rather meaningless for lots of reasons.
For example, because of the huge amount of genetic diversity in Africa, two people from two different African nations will have less in common, genetically, than a European and someone from an African nation. And yet the average person would most likely guess it was the other way around.
Perhaps because humans are very visually orientated, however, we have now becomes fixated on skin-colour, and using that to define "race". Unfortunately people don't understand that there is little or no biological basis for any other traits, beyond skin colour. For example, The gene for skin-colour has no relation to things like musical ability, eye shape, athletic ability, etc.
Genetic traits are measurable, and often have other effects on a person (blonde people are more likely to have fairer skin, and so get sunburned more easily, etc), but other traits are stored in completely different areas of the human genome. A good way to look at it is to remember that skin colour is as biologically significant as hair colour or eye colour. The biggest mistake is thinking that "race" means something more significant about someone more than just "shared genetic history".
Until people understand that the difference between a black person and a white person is as biologically significant as someone who has freckles and someone who doesn't, common misunderstandings about the importance of race are likely to continue.
Most people don't even understand that "French" people are a race, for example, and I've even been "corrected" by people using it in that way!
In short: So much talk about "race" has placed far too much emphasis on the word, as if it means something significant. It doesn't.
And a billion other papers and research all saying the same thing.