Jumping into an old post. I was this week googling for an answer to the same question, so here is what I have understood from Specialized website. Perhaps this will help for some other fellow google-cyclists in the future
R level = "level of modulus of the carbon fibers". R value refers to the "stiffness of individual fibers within the carbon matrix", so it the higher R the stiffer and more efficient is the particular carbon material. So, when the level is higher (R11 > R8), they can utilize less material in order to create a Specialized bike frame of the same or higher stiffness. Compared to the frames with less modulus carbon fibers.
Bottom line
Each level or R of the carbon frame takes off 100 to 150, to even 200 grams of weight (11R lighter than 10R or 8R) and at the same time the ride will be either a little bit stiffer or more vibration-absorbing, depending on the type of bike (Tarmac/Roubaix).
