At first, GISs used vector data and cartographic spaghetti structures. Points, lines, and areas can each be stored in their own files, with links between them. Arc junctions are only at nodes. Vectors just seemed more correcter. TIN must be used to represent volumes.
Vector can represent point, line, and area features very accurately.
Vectors are far more efficient than grids. Vectors work well with pen and light-plotting devices and tablet digitizers. Vectors are not good at continuous coverages or plotters that fill areas. Topology allows automated error detection and elimination. Rarely are maps topologically clean when digitized or imported.