Each show has a theme to it and often emotion is felt from the characters whereas old school circus shows would run one act after another with no real tie-in, underlying message, story, or theatrics, which is less likely to captivate an audience.
Varekai, for example, is loosely based on the Greek myth of Icarus, the story of the boy who flew too close to the sun. But rather than fall to his death as Ovid's Metamorphosis suggests, in Varekai, he falls into an enchanted forest, wounded and scared.
Even one simple Cirque du Soleil act can contain a deeper social commentary. This clip from Midnight Sun, for example, implies a man breaking free from the rat race, going outside the "box" and into a new reality.