Each of the 6 races has their own WAR Story, starting from prologue and ending in chapter 22. Warcamps are also chapters (without numbers) in the 'story'. All have three influence rewards, which are able to be recieved for each 1/3 of the total influence for the chapter is gained. Pick up your rewards from that chapter's rally master.
You are able to complete other races WAR Story of your own faction. Note that each career gets its own list of rewards to choose from for chapter influence rewards.
The WAR Story is split into Tiers and Chapters. You can also find 2 sections for dungeons per faction.