[every man with his band]: All of the indications we have seen in the Jaredite record indicate that clans controlled the government, an arrangement that is well known in history, and certainly present in the later Mesoamerican cultures. Here we learn that the organizational principle of the kin-group was present even inside the larger polity. Of course this model continues throughout Mesoamerican history, and is seen in the Nephite history as well.
In this case, we learn that the disruption of the larger political structures has so altered the nature of rule that the kin-groups are splitting up and relying upon their own internal structures rather than a larger political institution. This is similar to what happened among the Nephites with the political structure was removed. Lacking that larger organizational principle, the kin-groups become prominent, and the built-in leadership in the clans became the organizational principles.
[fighting for that which he desired]: While we are not told what it is that they desired, it can be understood that for most of these kin-groups, the fight was for their ancestral lands and the ability to use that land to produce their food.