Let's imagine you wanted to know how many marbles are in a jar but you couldn't count them all. Instead, you could take a random sample of marbles from the jar and count those marbles. Then you could use the information from the sample to make an estimate of how many marbles are in the entire jar. That's kind of like what a Watterson estimator does, but instead of marbles, it's used in biology to estimate genetic diversity in a population.
In biology, there are little pieces called genes that make up an organism's DNA. These genes can come in different versions, called alleles. The more alleles there are in a population, the more genetically diverse that population is.
But just like with the marbles in the jar, you can't always count all the alleles in a population. So instead, you take a sample of organisms from that population and count the number of alleles that are different in that sample. Then you plug that number into the Watterson estimator formula, which takes into account the size of the population and the number of organisms in your sample, and gives you an estimate of how many alleles are in the entire population.
This can be really helpful for scientists to quickly estimate genetic diversity in different populations and compare them to each other.