With the improvement of agriculture and farming, this caused a lot more food and crops to be made. Since there was more food being made, there was just too much to deal with, this lead to the development of government.
With all of the new food and crops, there needed to be a set of people to control and manage it. These people would manage the crops, along with controlling the sales and trades that went along with it. This ended up going further into other things over time.
Along with more people getting into agriculture and farming, and the new surplus of food, people needed protection. The government could offer protection to the people and their farms, which is also another example of how improved farming lead to the development of government.