What is "war rank has increased?"

As time goes by in the game, you will gain "war score".  Your war score will increase faster the more flags you control.  When you get enough war score, your team will increase in war rank.  The max war rank is 10.

In order to purchase certain citadel upgrades, you need to meet the war rank requirement.  You'll see the required war rank at the top of the citadel upgrade purchase screen.

To check your war score and war rank, press tab.  I think you go up in war rank every...720 war score or something like that.  I can't remember the number for sure.

Every 810 points.

War rank is pretty important as well as citadel upgrades.  Hold the flags and you'll jump ahead of your opponents in war rank.  This lets you access Priests, Angels, Cats and Giants before they do.  It can be a game winner.