The predecessors to solid state devices were vacuum tubes. There, the electrons were traveling in the vacuum between the cathode and the plates, and being modulated in various ways by the electric fields from voltages on various plate arrangements.
The term "solid state" refers to the fact that the electrons in semiconductor devices are traveling through the solid matrix of the atomic structure of the material. As already stated, the diode and transistor (BJT, JFET, MOSFET) are the basic structures. But even exotic stuff like superconductivity can be considered a solid state phenomenon.