What is the best way to describe the function of a typical transistor in an electronic circuit?

A transistor in a circuit can do many things. It can be used to amplify voltage signals, or current signals, create current and voltage sources, make buffers, and so on. Transistors also find a major use in logic circuits (ie, where signals can either be a '0' or a '1'), where they essentially act as a switch, and can be used to create inverters, AND gates, OR gates, and all sorts of useful components.

By itself, a transistor is a three-terminal device that can control the current going through two of its terminals through the voltage applied at the third terminal.

But there are many applications for a transistor in its many different configurations, which is why it is so important in modern electronic technology.