Put simply, if you're using the D4 to take a steady stream of photos, Nikon's contention is the EN-EL18 will give you more frames per charge than would have been possible with the EN-EL4a. Conversely, if the camera is kept awake but is spending far more time idle than it is taking pictures, the EN-EL4a would last longer on a single charge than the EN-EL18.
Akagi cites two reasons for the EN-EL18's emergence. The first is straightforward: a new battery, and new charger for it, was required to be compliant with new battery regulations in Japan. The second is that Nikon sought to build a battery that would not only meet their home country's revised regulatory requirements, but would also surpass the performance of the EN-EL4a.