Old English bæc "back," from Proto-Germanic *bakam (cf. Old Saxon and Middle Dutch bak, Old Frisian bek), with no known connections outside Germanic.
The cognates mostly have been ousted in this sense in other modern Germanic languages by words akin to Modern English ridge (cf. Danish ryg, German Rücken). Many Indo-European languages show signs of once having distinguished the horizontal back of an animal (or a mountain range) from the upright back of a human. In other cases, a modern word for "back" may come from a word related to "spine" (Italian schiena, Russian spina) or "shoulder, shoulder blade" (Spanish espalda, Polish plecy).
To turn (one's) back on (someone or something) "ignore" is from early 14c. Behind (someone's) back "clandestinely" is from late 14c.
To know (something) like the back of one's hand, implying familiarity, is first attested 1893. The first attested use of the phrase is from a dismissive speech made to a character in Robert Louis Stevenson's "Catriona":
The story, a sequel to "Kidnapped," has a Scottish setting and context, and the back of my hand to you was noted in the late 19th century as a Scottish expression meaning "I will have nothing to do with you" [e.g. "Jamieson's Dictionary of the Scottish Language"]. In English generally, the back of (one's) hand has been used to imply contempt and rejection since at least 1300. Perhaps the connection of a menacing dismissal is what made Stevenson choose that particular anatomical reference.