Communities remain in the same spot. Farming leads to the development of new technology. New skills lead to a greater division of labour. Individuals specialise in certain types of work, be it tool making, leatherwork or defence. However the key difference is that farmed land becomes a valuable resource.
Land provides a surplus, that is land provides more food than is necessary for day to day survival.
More importantly, land will provide this resource in the future, for the next generation. None of this is true of the herd of wild animals persued by the hunter-gatherer. The concept of ownership developed. So civilisation began when man began to acquire wealth in the form of land, food and animals. If a rich man wants to ensure that his offspring alone inherit his wealth, he must be sure that his wife is only mating with him.