Hi,
Factions are groups of people that have the same beliefs, or whose beliefs overlap. Something that is makeshift is something that has been put together quickly, usually because there was no other choice.
Therefore, "how war is increasingly factionalized and makeshift" means that war is more often being fought by these 'belief groups' in the best way they can at the time, rather than a structured army with a chain of command, reliable weapons, and modern resources.
Hope that helps :)