The implicit method of representing surfaces uses a single-valued function of three variables. The surface is the locus of points for which the function has some constant value. If that value is taken as zero, then the surface represents the interface between regions of space having negative values and those having positive values. Such surfaces are also called zero sets or level sets.
Implicit surfaces (also called level surfaces) are more fully described on the Level Surfaces page. SolSurf is an example of software which uses the implicit method to generate surfaces.