The taking in and letting out that keeps a body alive. Its root is the same as soul and animation — to breathe into is to give life.
Old English braed (odor, vapor, exhalation), from Proto-Germanic *brae-tho, of debated deeper origin; the widespread pattern that makes Latin spiritus and Greek pneuma mean both 'breath' and 'spirit' sits behind this word too, even if English arrived at 'breath' by a slightly different road.
The taking in and letting out that keeps a body going — carrying, as breath does in many languages, more than air alone.