With surface modeling you build a shape face by face. Faces made by surface features can be knit together to enclose a volume, which can become a solid. With solid modeling, you build all the faces to make the volume at the same time. In fact, solid modeling is really just highly automated surface modeling. Obviously there is more detail to it than that, but this definition will get you started.
You can drive a car without knowing how the engine works, but you cannot get the most power possible out of the car by only pressing harder on the gas pedal; you have to get under the hood and make adjustments. In a way, that is what working with surfaces is really all about — getting under the hood and tinkering with the underlying functionality.
The goal of most surface modeling is to finish with a solid. Some surface features make faces that will become faces of the solid, and some surface features only act as reference geometry. Surface modeling is inherently multi-body modeling because most surface features do not merge bodies automatically.
In the end, you may never really need surfaces. It is possible to perform workarounds using solids to do most of the things that most users need to do. However, many of these workarounds are inefficient, cumbersome, and raise as many difficulties ...