You're right to be confused, because that passage is extremely ambiguous. It looks like the author omitted whatever Pääbo said before “Our job is to find out which of those 30,000 are most important, because they tell us what makes us uniquely human”, where he presumably clarified what "those 30,000 [things]" actually are, and I haven't found a reference to the 30,000 figure in Pääbo's major publications.

Therefore, I'll have to make my best guess about what the 30,000 and 3 million figures signify. The first refers to variations between groups (all humans and all Neanderthals), while the second refers to variation within groups (individual humans). The number of differences between two humans has a straightforward interpretation: it's simply the number of nucleotides in two people's genomes which are not the same at each location. This intra-group variation is important to keep in mind, because it complicates the matter of calculating inter-group variation: if all humans are somewhat different, and all Neanderthals are too, how can we compare them?

Generally, we calculate the genetic variation between populations (which are different species in this case) by comparing the DNA sequences that are conserved (i.e. the same) within each population. For example, we'd find all the nucleotides that are shared among most or all humans and those that are shared among most or all Neanderthals, and then we'd compare those sets to each other and see how many differences there are between them. Those differences probably contain important mutations that, so to speak, make humans humans and Neanderthals Neanderthals. To use more technical vocabulary, we would say that these differences are alleles which are fixed (i.e. shared by all members) in each population.