Solid state guitar amps use transistors in the preamp and power amp to amplify an instrument signal. Transistors gained a bad reputation after their initial introduction to musical amplifiers in the 70s, but this was only because many of the first transistor amps were designed by cost saving engineers who did not understand the character that guitarists and musicians were after in their amps. What resulted were flat sounding thin amps, but this was because of how they were designed, not the transistors themselves. Today, there are many well-deigned, lightweight and musical sounding solid state alternatives, so you can get all the tone without the heft and cost of vintage valve circuitry! Solid state amps can be particularly good clean platforms for guitar pedals.