You will probably be interested in the American Association of Physical Anthropolologists' statement on Biological Aspects of Race. It's rather long and detailed, so I won't attempt to reproduce it here, and it's rather well written, so my summation wouldn't really do it justice.
In science, when we classify something, we need to have inclusion and exclusion criteria. You either carry a certain gene variant that has a deletion mutation that increases your risk of cancer, or you don't. To be a zebra, you need four legs and stripes. If you have stripes, but six legs, you're not a zebra. If you have four legs, but spots, you're not a zebra. So how then do you classify a race? Taking the three major old (and racist) classifications, people were either thought to be mongoloid, caucasoid, or negroid. How do you tell if someone is negroid? Well, their skin is dark brown! Caucasoids have white/pink skin. But where's the cutoff? How would you classify someone of Arab descent, with skin darker than a northern European, but lighter than a sub-Saharan African? How would you classify the offspring of a northern European and a sub-Saharan African?
People are a blend of phenotypes. While you can always define a group of people that look one way, and another group of people that look a different way, you'll always be able to find people somewhere in the middle. We are all the same species; every single fertile male on Earth can reproduce with any fertile female, regardless of social class, national or geographical origin, ethnicity, culture, skin color, or any other factor. This is not true of robins and cardinals, or elephants and zebras, or dogs and cats. (Yes, some species can form hybrids with other species, but that's a different topic.)
Within our species one can define certain groups based on physical characteristics, such as those of Han Chinese descent, that are grossly similar to one another, but far from identical. This group may share some common gene alleles, but there will still be (sometimes significant) variations from one person to another. One of the problems identifying that group as a race is that there is no strict biological definition of the term, with explicit inclusion and exclusion criteria, and the reason for that is it is almost impossible to identify these strict criteria that more than a handful of people would meet, due to the variation I mentioned earlier.
Now, of course there are groups of people with similar ancestry that share certain common gene variations that protect them from or predispose them to any number of diseases or conditions. There are also confounding cultural, socioeconomic, and environmental factors that make absolute connections between these gene variations and the associated diseases tough, as well (African-Americans and heart disease, native Americans and alcoholism, etc.). However, calling these different groups "races" is not helpful, and most of the time not even accurate (again, getting back to the lack of a clear definition of race).
Race is a social construct, based on a long and dark history of misguided attempts at classifying people. The concept likely has some utility to sociologists (I'm not one, so I don't know) so that people can voluntarily choose to identify with a group, and likely other reasons as well. However, because of the vagueness surrounding its meaning, and the incredible genetic diversity and identity between people, the concept really has no biological basis. I can just as easily study why people with certain genetic markers are predisposed to heart disease, for example, as I can study why many African-Americans get the disease, and I actually have a clearer criteria for subjects to include in the different arms of my study because I have a solid genetic definition, not just one based on skin color, which is completely irrelevant to the subject at hand.
