There are usually two methods for calculating variance. One is 1/n * sum((x-mean(x)2), whereas the other is 1/(n-1) * sum((x-mean(x)2) The second is an unbiased variance estimator, which R employs.
I think the remarks concerning sample variance vs. population variance are a little misleading. The population variance is commonly conceived of as the population's fixed, unknown variance. We want to estimate that variance, therefore we use a sample of the data to do so, hence the term sample variance (which can be estimated in more than one way, as mentioned above).