Carry is more raw energy hitting the pins. Good carry has the proper entry angle into the pins and the proper roll for deflection of the ball off the pocket, through the 5 and into the 9 (or 8 for lefties). Good carry also keeps the pins low to maximize their effective size. Too much speed, too sharp an entry angle, too much drive actuall reduce your carry.
To answer your primary question, why do new balls carry better--(as compared to the urethane balls of the 80s such as the original Black Hammer)
1) Resin is tacky. A resin coverstock has a low coeffient of friction on oil, so it skids easier. However, it is very tacky so it grabs the dry boards. The skid then grab provides more energy in the backend of the lane plus a sharper entry angle than most bowlers could create before resin. (FYI-plastic grips less on dry so you can't create the same entry angle or drive into the pocket.)
2) Particles add control. While pure resin coverstocks have the most power, they can be hard to control. Ading particles to the resin, gives the ball more traction in oil without diminishing much of the hitting power.
3) Flare adds potential reaction. To maximize the possibilities in the coverstock, new balls have cores with differentials that create flare. The flare increases the amount of coverstock used. This allow you to control the amount and shape of the hook.
4) Mass bias fine tunes reaction. Cores designed with enhanced mass bias add the ability to be very specific with the shape of the breakpoint. This is another step for controlling the entry angle.
--------------------
Good luck & good bowling