1680s, "large log placed at the back of a fire," from back (adj.) + log (n.1). Figurative sense of "something stored up for later use" is first attested 1883, but this and the meaning "arrears of unfulfilled orders" (1932) might be from, or suggested by, log (n.2).
1. There is a backlog of repairs and maintenance in schools.
2. We are faced with a backlog of orders we can't deal with.