Ok, i'll try to make that explanation as clear as possible - and please remember that i am not a biologist, but a physicist. If any one *who knows the subject better* has something to add or correct, please do so.
Much has been said in the old debate about human being, and the existence (or non existence) of races among them. A few decades ago, it was widely believed that skin color determined intelligence, behaviour, and even having or not a soul (i'm still skeptical about the scientific significant of this characteristic). More recently, in a honorable - but misleading - attempt to clear these ideas from people's heads, schools have been busy teaching the non-relevance of the idea of "races" among humans.
Here is what i understand is true :
-> Skin color is determined by very few genes. For any given individual, it is possible to possess (and express) any existing version of these genes, without having a significant impact on the other physical characteristics (phenotype).
Therefore, just knowing someone's skin color does not give you any information on the rest of his/her genes. Provided that you don't know anything else about the person ! If you add other informations, everything changes : you can safely assume that a black person living in north america has a high probability of having african origins.
-> For any given skin color, there are many people (with different genetical backgrounds) in the world who have that color. The set of "people with a very black skin" is not equal to the set of "people from african countries where people have a very black skin". You also have to add native australians, some indians, etc..
-> Similarly, even if you assume that genetics determines everything, including intelligence, behavior, and the size of your penis (note that this opinion is not supported by the majority of the scientific community), saying that someone is "white" does not describe the person accurately. It's a drop in the water.
-> Despite all the above, it is misleading to state that there is no more genetical difference between two given people of a given "race" than between two people taken at random. The reason is simple : When two people have sex, the baby has genes from both his parents. Not from the neighbors, not from overseas (lol, unless an accident happens !). In parallel, evolution takes place.
[evolution is based on two processes : natural genetic variability because of DNA replication errors and other accidents including DNA borrowed from virii, and natural selection]
The thing is, evolution might seem slow, but it was fast enough for significant changes to appear in some populations before humans started to have cars and airplanes. For instance, the peculiar mongoloid eyes, skin colors, and resistance to some diseases. But that's only a small sample.
Therefore, until recently, isolated populations did have quite different gene pools. (okay, not as different as between a human and another monkey !). Some genetic characteristics tend to occur more frequently in some ethnic groups than in others. In other words, it is still meaningful to distinguish ethnic patterns inside the human race, based on their geographical origin (and not on their skin colors) - but it won't be as simple in a few years when having babies with anyone on earth will be just as easy as with your neighbor.
My opinion is that such patterns will emerge /again/ when the human race will colonize space, because it won't be as easy to go to mars and back again as travelling from NY to Mexico
Please remember that i am only talking about patterns - humans like simple ideas, and putting patterns into little closed boxes. It is all too simple to make races out of these ethnic patterns, and then be puzzled when some people obviously don't fit in any of these boxes...
As for me i don't see any reason to be offended by the question - i'm sure the lady didn't mean to be rude to anyone.