A transistor is a device made from semiconductor materials that can do three things: amplify a signal, open a circuit, or close a circuit. It has at least three terminals used for connection to an external circuit; basically, in a three terminal suite, you can control the voltage between two terminals by applying voltage to the third. You can also make an external switch, which can also be controlled by another external switch, and so on. The possibility of doing these “cascades” allows us to build extremely complicated logic circuits, which are the core of the computer you are using right now.
The power transistor paved the way for pretty much every electronic device developed in the past 50 years. It is the building block of integrated circuits, that can have over 1.000.000 transistors per square centimeter. This means that it can be quickly turned on and off at 0.000000001 seconds, and things continue developing each year. Without the small transistor, the world as we know it today could never exist.