Other forms: verging; verges; verged
Think of an edge, a border, a boundary, and you are thinking about the verge, the point where something begins or ends.
We talk about a nervous person being on the verge of a breakdown, or about a scientist being on the verge of a major breakthrough, but the British have another good physical meaning: they call the strip of grass that borders a walkway the verge, giving you a clear mental picture that goes beyond the abstract.