This surface is some mathematical surface (i.e., a function given by ) that defines the interface between two bulk liquid phases. Given that the interface itself is a concept that is blurred at the molecular scale, the definition of the surface varies depending on the author. Sometimes the choice is to take the Gibbs dividing surface.
Capillary wave theory proceeds by studying the fluctuations of this surface; many of its predictions are independent of the particular choice (like, e.g., the divergence of roughness with the area), but of course any microscopic detail will depend on the choice of surface.
The intrinsic sampling method is a recent approach to obtaining this surface from a molecular simulation.