First, he divided people into a hierarchical scheme:
population--> race--> species (Home sapiens)
A population is a distinct group of interbreeding people, often associated with geography. For instance, a population might be the group of people living in a single town. A race would therefore be a larger group of people to which several populations belong. For his paper, Lewontin classified populations into 7 races: Caucasian, African, Mongoloid, S. Asian Aborigines, Amerinds, Oceanians, and Australian Aborigines. The final level was Home sapiens itself. The hierarchical setup is necessary to make the "within race/between race" distinction. Arguably, individuals within a population will be more genetically similar to each other than to another population. This makes sense since they are living in the same environment, breeding with each other, etc. If race is an important factor, then populations will be more genetically similar to other populations within the same racial group than to populations in a different racial group.
Looking at it from another direction, let's say I have Population A in Race X. It has a genetic diversity of 1 (this is a made-up number that doesn't mean anything real; assume that the lower the number, the lower the genetic diversity). Population B of Race X has a genetic diversity of 1 as well. When I mix the data from Population A and Population B together, I get a genetic diversity of 4. This makes sense if Population A and Population B are genetically similar within the populations but there are differences between the populations. If racial groupings can be determined using genetics, then I would expect that if Population A was from Race X but Population B was from Race Y, then the genetic diversity would increase a lot (to, say, 87).
Clearly, then, everything hinges on what we mean by genetic diversity. In Lewontin's paper, he looked at 17 different polymorphic loci. Essentially, this means that he looked at different regions of DNA which can show differences between people. Note that I didn't say "genes." A polymorphic locus does not need to be connected to any gene (though it can be). It simply must be a stretch of DNA which is sometimes different in different people. Each different version of the locus is called an allele. Looking at many different loci makes it more likely that you'll be able to find real differences or similarities, rather than an anomaly that might exist at a single locus. To determine diversity, he looked at the frequency of the alleles at each locus. The more alleles there are, the more diverse it is (because there are more versions of the locus); the more equal the frequencies of the alleles, the more diverse the population (because if one allele was at a very high frequency, then more people would be the same, leading to less diversity).
After some number crunching, Lewontin found:
The mean proportion of the total species diversity that is contained within populations is 85.4%.... Less than 15% of all human genetic diversity is accounted for by differences between human groups! Moreover, the difference between populations within a race accounts for an additional 8.3%, so that only 6.3% is accounted for by racial classification.
What does that mean? When you start off with a single population, there will be a certain allele frequencies for each gene, and there will be a certain number of alleles in the population. When you pool another population with the first, you would expect a change to the allele frequencies and the number alleles unless the populations are very similar. As you add more populations, you would expect more diversity. Once you pooled all of the populations together, that should be the maximum diversity. So, when Lewontin found that 85.4% of total species diversity was found within a population, it means that when you look at a single population, 85.4% of the maximum diversity was already there. Add in more populations within the same race, and that accounted for another 8.3%. If you pooled all the races together, that accounted for the last 6.3%. Lewontin goes on to conclude:
It is clear that our perception of relatively large differences between human races and subgroups, as compared to the variation within these groups, is indeed a biased perception and that, based on randomly chosen genetic differences, human races and populations are remarkably similar to each other, with the largest part by far of human variation being accounted for by the differences between individuals. Human racial classification is of no social value and is positively destructive of social and human relations. Since such racial classification is now seen to be of virtually no genetic or taxonomicsignificance either,no justification can be offered for its continuance.
Though this seems cut and dried, it's not the entire picture. Check out Part II - Lewontin's Fallacy.
1. Lewontin RC. The apportionment of human diversity. In: Dobzhansky T, Hecht MK, Steere WC, editors. Evolutionary Biology 6. New York: Appleton-Century-Crofts. 1972. p 381–398.