I think circles are place where there are some troops, when in far, circles will also be in place of pixels conquered, thats why in fighting there is so much circles(this is just my thinking, i am not sure if its true)
the ai will send armies to the border. once they gain clear land they gain more armies, the little black circles when you click show armies you'll be able to see them. They will go and fight other armies and conquer the other country and achieve total world domination.