IPA: //ˌæfɪˈdeɪvɪt//
KK: /ˈæfɪˌdeɪt/
A written statement that someone swears is true, usually made in front of a legal official.
He submitted an affidavit to support his claim in court.
Affidavit is formed from "affidare" (meaning to pledge or declare) and the suffix "-vit" (from the Latin root "vita", meaning life). The word refers to a written declaration made under oath, essentially pledging the truth of the statement made.
Think of making a 'pledge' ('affidare') to tell the 'truth' in a written statement — that's what an affidavit is.