I've seen order parameter used in two different ways. One is to distinguish between an ordered and an unordered phase, like whether the net magnetization is stable or not. The second way is to distinguish what the magnetization is, up or down.
More broadly, does it just mean a macroscopic observable? For us to see it at large scales, doesn't it have to be relatively stable?
EDIT: by macroscopic observable I mean like the net magnetization, which is an average of a local operator.