Diamond says that the islands of Polynesia were a natural experiment because they were all settled by people of one culture and ethnicity. This is, therefore, an experiment about how important culture is in determining how a society develops. Some people believe that societies develop as they do because of their culture. They believe that some societies have cultures that are more conducive to development while other societies have cultures that hold them back. If that were the case, all of Polynesia should end up with the same kind of society because it was all settled by people with the same culture.
However, the societies of the Polynesian islands were not all identical. Diamond compared the societies with some environmental variables that are listed on p. 58 in the paperback edition of the book. He looked at climate, geological type (atolls, high islands, etc.), marine resources, terrain fragmentation (whether the islands are split up by ridges), and isolation. This made the settlement of Polynesia a natural experiment. If, for example, all of the societies on atolls were similar while all of those on high islands were similar to one another (but different from the atoll societies), it would show that the geological type helped to determine what sort of society arose.
Thus, the environmental differences allowed Diamond to create a “natural experiment” in which he could try to determine what factors affected how societies developed.