This definition cannot actually be used since there are no postulates to go along with it to connect the edges of a surface in any way to the surface.
Euclid uses the same term for the end of a line in I.Def.3, the edge of a surface in this definition, and the surface of a solid in XI.Def.2. That term could be translated as "that which is around," "the limits of," or "the extremities of," but in English the terms "the ends of" a line, "the edges of" a surface, and either "the surfaces of" or "the faces of" a solid are fairly standard for different dimensions.