means The edge, border, or brink of something — the point just before a state or place begins.

from From Latin 'virga,' a rod, twig, or wand. In medieval usage the verge was literally a staff of office — and the area of jurisdiction it commanded, the ground 'within the verge' of an official's authority. From that bounded zone the word drifted to mean any boundary, then any edge, and finally the figurative brink: to be 'on the verge' is to stand at the rim of what's coming. (The same 'virga' also gives us 'verger,' the church official who once carried that very rod.)