Solid State Amplifier

Even though transistors were first used in commercial radios in the mid 50s, and later also other products, tubes were the still standard for many years. Besides, amplifiers could only rely on tubes if any power was needed. Therefore, 'solid state' amplifiers with higher power came eventually, as better high effect transistors were produced.
The term solid state itself became used when the transistor amplifier market advanced in the late 60s into the 70s. With the phrase put on products, potential buyers were shown that it was "new" technology and no vacuum tubes inside, simply, a modern design.
Although the term "solid state amplifier" was first used for hi-fi amplifiers, it is still used, for audio amplifiers as well as high power HF/linear amplifiers to increase the output power from radio transceivers or transmitters.

Even though transistors amplifiers are by far the most common, there are still tube amplifiers used and manufactured. Tube amplifiers are used with respect to the " tube sound". In that view, many old tube amplifiers have become even more valued.

Links:

The Tube vs Solid State Amp debate is slowly but surely coming to an end! - Epinions.com
What makes a good Solid State HF Amp?
Solid state guitar amplifiers - Wikipedia
About the sound of tubes vs. solid state amplifier sound - Wikipedia