I don't do eukaryotes, well humans anyway, but in population genetics an allele frequency of zero simply means it is present in no individuals against the reference allele. It doesn't mean the allele is heterozygous nor homozygous its simply absent. Whether that is informative or not is an interesting question. In addition, it does not necessarily mean the allele is rare, it is simply absent against the population in your analysis. The sickle cell anaemia allele is not rare, in certain parts of Africa it has high frequency, but it would be absent if all the individuals in the population of the analysis that did not have African ancestry. In this specific example, it would likely reflect inaccurate sampling of the population in the analysis.
If allele frequency was 1 it would mean complete homozygosity and identity, which is very informative.
I'd simply refer to the wiki which is pretty good for this. Allele frequency is the entire basis of population genetics.