Because you tagged this with "Chapter 14" and "Guns, Germs, and Steel" I assume that you are asking about this question specifically in the context of that book. I have moved your question and will answer it based on that.
In Chapter 14 of the book, Diamond argues that governments are created when the population of a given group becomes too large to be controlled in traditional ways. Traditionally, people in a group did not kill one another or otherwise offend one another because they were tied together by bonds of kinship and friendship. Everyone in a group of people was either related or at least connected to one another by mutual friendships. In such a situation, you wouldn't steal from someone else or kill them because you have connections to them.
When a society's population gets big enough, though, these connections disappear. Even in a small town like the one I live in, there are about 20,000 people. I see many people every day that I am not related to and do not know. There is no social mechanism to keep me from attacking such people or having conflict with them that would boil over into something very bad.
Therefore, when a society's population gets to be big enough, it needs a government. It needs some authority to prevent people from harming one another now that they are not tied by kinship or friendship. This is why governments are created--to serve this need.
At its most basic level, humans have a need for safety and order. Without any government at all (anarchy) the rules are made by those with weapons, and whoever has physical control over the land at the moment. Check out Somalia if you want a picture of what its like to live that way. The average Somalian, by the way, dies 32 years younger than the average American.
Out of this need for safety and order comes agreements and arrangements among groups of people, similar to the Mayflower Compact, where everyone agrees that decisions and rules must be made, and a system is required to do that. In the absence of those agreements, dictatorships usually arise.