The ostensible purpose of Guns, Germs and Steel is to come to understand how and why white European civilizations came to dominate the entire world, displacing native peoples and their cultures, when all humans are approximately equal in terms of intelligence and should therefore, hypothetically, not have exhibited the extreme differences in technology that were observed when pitting high-tech Europeans against low-tech natives.
Government is detailed in Chapter 14, titled "From Egalitarianism (equality) to Kleptocracy (theft)". Diamond argues that government, in various forms, is a response to the issues faced by the group being governed, which largely depends on its population size; a large state is significantly different in terms of its size, organization and problems compared to a small band of 20 people. Large groups are almost always organized into states because it is virtually impossible to address their problems, such as conflict resolution, with the governing system of a smaller group.
This, however, does not answer how large governments came to be in the first place. Diamond feels that the transition from smaller, non-state governments to large ones is brought on only by conquest, or an alliance sparked by the threat of external force; he sees no examples wherein a group of small, independent governments voluntarily sacrificed that independence for economic gain.
So; governments formed organically, in response to their population size, and did so in order to manage the problems that population generated, which differed depending upon size.