The exact influence of DNA on intelligence and other aspects of behavior is not yet known in much detail. It almost certainly has some influence, though.
The racist view is that this influence is so great, and the differences among the races therefore are so great, that race should be the central organizing principle around which we view the world.
To the racist, all -- or most -- major social phenomena can be explained via the differences in the races.
Now there are certainly differences among the races, if we are talking about behaviors we can attribute to aggregates of people. Whether these differences are simply the unavoidable expression of innate drives, not subject to serious modification by social institutions, is a different question.
The Indians of Guatamala are a fairly inert bunch today. You don't look to them for advances in astronomy or architecture or mathematics. But these people bear the genes of the Maya, who were pioneers in all of these fields.
The Danes today are the nicest people in the world. Their genes were borne by the Vikings.
Something happened to both of these peoples, to alter whatever genetically-based drives they have.
It's not that race -- DNA -- plays no role in understanding behavior. It is just not the all-important one which dominates everything else.
Racists make the same conceptual error as extreme feminists. I don't know if any of the latter are around today, but when I was young(er), these ladies were quite vocal: they saw all of human history, and everything in present-day society, through the lens of our sex (or "gender" as we are suposed to call it now). The whole of human history was the history of female enslavement to the Patriarchy. All of present-day society was a male conspiracy to make women childlike, emotional, and dependent on men. Even language embedded male-supremacist assumptions. Science itself was a male-warped enterprise. And so on.
Now, the thing is ... the extreme feminists weren't entirely wrong! (For a sobering experience, read Susan Brownmiller's[ame=http://www.amazon.com/Against-Our-Will-Women-Rape/dp/0449908208/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1200675078&sr=8-1] Against Our Will[/ame]. She is not the most extreme of feminists, but she definitely sees the world through a feminist lens. And much of what she documents is true. Incidentally, anti-Black racists will appreciate how a strictly feminist approach can bring otherwise leftist people into congruence with their own outlook, when they read her attack on[ame=http://en.wikipedia.org/wiki/Emmett_Till] Emmet Till[/ame], the young Black man murdered in Mississippi in 1955 for wolf-whistling at a white woman.)
No, the feminists were not entirely wrong. Just like the racists today -- Black and white -- are not entirely wrong when they call attention to the crimes and failings of the race they don't like.
But they are far from being entirely right, either. They see the world through a particular lens, and ignore all the multiplicity of other factors that must be taken into account if we are to understand how human society works, and how it may be made more congenial for us.
I used to see the world this way, although my special monocular vision was refracted through the lens of economic class and the class struggle. It is comforting. Like a good classification scheme, it helps you arrange your knowledge. It tells you where to look for information to support your viewpoint.
And seeing the world this way is very economical. You are acutely attuned to all evidence that supports your view. You filter out, explain away, push aside, or twist to your own purposes all evidence that does not. You don't have to do nearly as much mental work as someone whose understanding of the world is trying integrate many factors, instead of just one.
But it leads to wrong results. The extreme feminists wanted, in effect, women to withdraw from male-dominated society. The racists want to separate the races. The Marxists want to eliminate social class by making us all employees. None of these visions is practical.
We are all stuck with each other, and we'll only escape when we pass on to the next world.