1. <operating system> A task running in the background (a background task) is detached from the terminal where it was started (and often running at a lower priority); opposite of foreground. This means that the task's input and output must be from/to files (or other processes).
Nowadays this term is primarily associated with Unix, but it appears to have been first used in this sense on OS/360.
Compare amp off, batch, slopsucker.
2. <jargon> For a human to do a task "in the background" is to do it whenever foreground matters are not claiming your undivided attention, and "to background" something means to relegate it to a lower priority. "For now, we'll just print a list of nodes and links; I'm working on the graph-printing problem in the background." Note that this implies ongoing activity but at a reduced level or in spare time, in contrast to mainstream "back burner" (which connotes benign neglect until some future resumption of activity). Some people prefer to use the term for processing that they have queued up for their unconscious minds (often a fruitful tack to take upon encountering an obstacle in creative work).