How did the ability to domesticate animals help a civilization's ability to become powerful and rich ?

The domestication of animals provides a handy source of food, meat and dairy products, in one place, allowing people to settle in that place, no longer expending all their energy on traveling for game to sustain them.  Concomitantly, if one is settled in one spot, one can grow food, which has the same consequence, less time and energy moving about foraging for food. When people stay in one area, they are inclined to build permanent structures, homes, shelter for animals, places to store excess food.  They begin to have a greater sense of community in one place, as well, and the elimination of the need to travel far and wide for food allows for a little more "specialization" of tasks.  In combination, these elements set the stage for community structures to be built, religious institutions and community storage facilities, for example.  Infrastructure emerges, means of dealing with sewerage, paths or roads, the community well.  All of this leads to what we think of as civilization.