The independent evolution of farming and the domestication of animals has contributed greatly to the uneven development of civilization across the globe. This is not meant to suggest that humans in areas of the globe that experienced a slower growth of civilization (the growth of urban areas and arts and crafts associated with this development); indeed, human beings have shown remarkable adaptability in working with the limitations that geography and climate impose upon them. The remarkable complexity of the Agricultural Revolution is demonstrated in this video.
The domestication of plants was usually a hit and miss proposition, and most of probably began as the cultivation of wild plants that by irrigation and accident became domesticated. Horticulture and husbandry (the domestication of animals) grew together; the domestication of bovine animals like oxen and cows eventually permitted humans to attach plows to them, and pull these through fields. This allowed humans to further intensify agriculture--that is, to grow the same amount of food within a smaller area. The intensification of food production is what permitted agriculture to become more attractive to large numbers of human beings around 7000 to 10,000 years ago, because this intensification allowed other human beings to devote their time to perfecting crafts, arts, and social practices (like religion) that enriched the societies that they were forming.
The domestication of animals and the development brought unintended consequences as well, of course--and not all of them have been beneficial to man. Chief among them are the development of virulent diseases like pox, plague, and influenza--all of which humans only developed after domesticating animals. Cattle, pigs, and chickens all are afflicted with diseases that are easily transmitted to humans. With humans also living in cities, in close proximity to one another, they can then transmit these diseases to each other. In addition, humans create a great deal of waste, from the food they consume (both excreted and the waste that is not consumed and disposed of as garbage) that animals like mice and rats are willing to consume. The fleas these small animals are host to transit disease, as well.
This bit of video comedy is, of course, played for laughs, but has certain truths about living in early cities, as well. The early undertaker knows that the appearance of someone "without shit all over him" means that he is someone of importance (the mythical King Arthur), because people disposed of their waste by simply throwing it out in the streets (it's how archeologists are able to find it). By creating these pathogens, humans living with these domesticated animals often shortened their own lives--but the eventually allowed their descendants to develop immunities and resistance to these diseases, and to pass these diseases along to people who had not developed these immunities.
The point to take away from this discussion is, I think, that civilization, while it does provide great benefits to mankind (in my own self interest, I would not have a job teaching history without it), those benefits come at great costs--both in personal freedom for individuals, and to the environment. Try to keep this in mind as we explore the evolution of human society in the coming months.