As far as I have seen used here on ballreviews, there are 2 meanings that are used indiscriminately, without description, so it's hard to know what people really mean:
1. They mean the ball has a stronger backend than the "other ball", and
2. They mean the ball hooks more AND handles more oil than the "other ball".
To my mind, when you say "stronger", it should always mean ball "A" handles more oil than ball "B". With resin balls, the amount a ball hooks has nothing to do with the amount of oil it can handle. (With urethane balls, it was true that the more it hooked, the more oil it handled.)
A stronger backend is not necessarily always a better ball. It can mean it leaves more washouts and more splits than a ball with less backend.