Cost Index (CI) is nothing new - most Flight Management System have been using it in some format for years.
The lower the CI, the more "importance" the machinery places on saving fuel. Low cost indexes will result in lower climb speed, (both indicated and mach), lower cruise speed, a generally higher cruise altitude, a later descent and a slower descent mach/speed. The higher CI's will result in the opposite.
A given cost index will result in a specific still air True Airspeed at altitude - however, it is normal for the FMS to adjust the mach number (MN) by .01 when the head wind or tail wind components exceed a programmed threshold value - ie, the airplane will slow down with a tail wind, speed up with a headwind (automatically) by .01 mach in an effort to minimize the fuel burn. More sophisticated flight planning programs will show this change on a leg by leg basis and will file the speed change as part of the ATC flight plan.