Choice B is the best answer. In the last sentence of the third paragraph, the author states that "computers and technology . . . are becoming virtual extensions of our memory." In other words, computers and technology are becoming memory sources that serve as additions to human memory. Thus, "extensions of," as used in the passage, most nearly means additions to.
Choices A, C, and D are incorrect because in the context of the passage, "extensions of" means additions to, not delays in (choice A), lengths of (choice C), or developments of (choice D).