A solid always knows what's inside and outside of itself. A surface, by default, doesn't — and that single fact decides whether you can get a mass property, a mesh, or a machining toolpath out of it directly.
New CAD users often treat "surface modeling" as simply the harder, more advanced version of "solid modeling" — something you graduate to once you've mastered extrudes and revolves. That framing misses what a surface actually is mathematically. A solid body is a watertight, closed volume — every point in space is unambiguously inside it, outside it, or on its boundary. A surface is a mathematical sheet with zero thickness and, critically, no defined inside or outside unless enough surfaces are stitched together into a fully closed, gap-free shell. Surface modeling exists because some shapes — a car's exterior sheet metal, a turbine blade's aerodynamic skin, a bottle's complex blended form — are far easier to define and control as a network of connected sheets before ever committing to a closed solid.