1. (British) comfortable, content. This vogue term of the early 1990s probably derives from the notion of a homeless person comfortably accommodated in a squat or a basher, etc., but was generalised to refer to any state of contentment. Made-up is a near synonym from northern English speech.

A new girlfriend and a flat and a car; I'm well boxed-up.

2. (American) intoxicated by drugs or alcohol. This usage may be related to the earlier 'boxed out', meaning uninhibited or wild (by contrast with the colloquial 'boxed-in').