Why is "Affidavit" an appropriate title for Chapter 45 of "Moby Dick" ?
An affiavit is a formal, sworn statement of fact. The title "Affidavit" is an appropriate one for Ch. 45 because in the previous chapter Ishmael reports some rather fantastic facts--that Ahab and Moby Dick have clashed before, that Moby Dick escaped and that Moby Dick and Ahab both hold a grudge against the other--that they are matched against each other for life. On its face, this seems like a fairy tale, but in Chapter 45 Ishmael swears some things that he knows to be true; among other things he relates that he has himself seen several instances of whales escaping the harpoon, that individual whales travel over a huge area and that the same whales have been sited in multiple places, and that individual sperm whales have been known to be very vicious.
Ishmael swears that "if the sperm whale, once struck [by a harpoon], is allowed time to rally, he then acts, not so often with blind rage, as with wilful, deliberate designs of destruction to his pursuers" (p. 175 of 2nd Norton Critical Edition). Here, Ishmael defends the story he is setting up, not as fiction, but as truth. He cites outside sources, writes as an educated man, and buttresses his story with the fact that he is a first person witness to whale behavior.
Melville uses the strategy of flipping back and forth between genres in his chapters. Some of them are fictional and narrate the plot of the novel, and some of them summarize and relate historical and scientific knowledge about whales (thus the term "affidavit"). You can read more about Melville's style by following the link below.