On the big Boeings V2 is well on the back of the drag curve. This means that if you go faster you have more excess energy to climb. Hence "improved climb" which is simply adjusting scheduled speeds (V1, Vr & V2) to stay on the runway longer and naturally faster to reduce drag in the segmented climbs after T/O.
Put simply, you "spend" the excess runway length to go faster rather than reduce thrust as much as is possible. This almost invariably improves 2nd segment climb limit weights (sorry, mass for you Poms!!) which tend to be the limiting ones enabling a greater payload to be lifted out of the port. Some operators are approved to use "Automatic Performance Reserve" too, which is simply a throttle push in the event of EFATO.
On the B744 the gain is trivial until the density altitude is quite high, but the theory holds water. Look at the old B747 classic specific charts out of, say, Harare.
Hello JT, please clarify my poor muddied explanations!!
