Wealth and power is acquired by years of hardwork and perseverance. It accumulates throughout a person's lifetime, but time is not so forgiving. A person can't enjoy their wealth forever; they must go through the natural state of death once their body has given up. So it is up to the next generation to inherit the wealth that was left by the previous generation and try to create even more wealth by using the inheritance (or not). And then once it is their turn, they too will pass it on to the next generation, and then the same thing will happen again, this cycle continuing until either the bloodline dies out or the wealth has run dry.
Those families that have managed to use their wealth well—either by investing properly, creating new technological advancements, running successful businesses, or by other means—become very influential. When they gain that influence, they would also gain notoriety from lands far and wide. And if they have amassed a great amount of fortune, their names can even be known all over the world, and in different languages as well. With their influence and wealth they would also naturally become powerful to a certain extent and even have the potential to create small ripples in sea of time that can end up becoming big waves changing the course of history.