Biologically, race is a subspecies within a species. The species that modern humans belongs to, Homo sapiens, does not have any subspecies so the term "race," in a biological respect, does not apply to modern humans. Race, however, is used as a socio-political category in many countries, including the United States. Historically, race has been used to create a hierarchy of races, with Caucasians at the top, but in current times, the term race has migrated away from this. Biologically, people of the same "race" can be very different from each other while two people of different "races" may be very similar.
On my application, there was a question for which "race" I am, but seeing as races do not apply to modern humans, I chose to not mark one.