The word "verge" has multiple meanings, depending on its context.
1) In a general sense, it can refer to something that is on or nearing the point of doing something; an action or event is imminent. For example, "We are at the verge of making a major discovery."
2) It can also mean the edge or border of something, especially when referring to landmarks or boundaries. For instance, "The park is on the verge of the city center."
3) In astronomy and physics, it refers to the outermost part of an object such as a planetary orbit or galaxy. An example usage would be: "The comet was at the verge of our solar system."