Old English bæc "back," from Proto-Germanic *bakam (cognates: Old Saxon and Middle Dutch bak, Old Frisian bek), with no known connections outside Germanic. In other modern Germanic languages the cognates mostly have been ousted in this sense by words akin to Modern English ridge (such as 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).
By synecdoche, "the whole body," especially with reference to clothing. Meaning "upright part of a chair" is from 1520s. To turn (one's) back on (someone or something) "ignore" is from early 14c. As a U.S. football position by 1876, so called from being behind the line of rushers; further distinguished according to relative position as quarterback, halfback, fullback.
To know (something) like the back of one's hand, implying familiarity, is first attested 1893 in a dismissive speech made to a character in Robert Louis Stevenson's "Catriona":
If I durst speak to herself, you may be certain I would never dream of trusting it to you; because I know you like the back of my hand, and all your blustering talk is that much wind to me.
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" [see Longmuir's edition of Jamieson's Scottish dictionary]. In English generally, the back of (one's) hand has been used to imply contempt and rejection at least since 1300. Perhaps the connection of a menacing dismissal is what made Stevenson choose that particular anatomical reference.