In the first paragraph of Passage 2, when discussing changing social relations, Mill writes that in her time there had come to exist "a just equality, instead of the dominion of the strongest." In this context of a society where some had once wielded much greater power than others, the word "dominion" most nearly means supremacy, or greater power.
Choices A, C, and D are incorrect because in the context of a paragraph discussing differences in the amount of power possessed by members of a society, "dominion" means supremacy, or greater power, not omnipotence, or the state of being all-powerful (choice A), ownership (choice C), or territory (choice D).