Skin colour is the main differentiation method used to specify race, in most cases. However, since the Human Genome Project, the concept of "Race" is redundant, as the percentage of our genetic material that affects skin colour is a tiny fraction of the total.
I have recently discovered that one of my Great-grandmothers was Jewish, which according to the Nuremburg Laws,makes me Jewish. That's another reason to throw the whole concept in history's rubbish bin too.
It would perhaps have been more useful to ask-"What is your cultural background?" That would have allowed for a varied responses from within countries too.