What is the role of field effect transistors in circuits?

The FET is a voltage-controlled device, and the distance between the drain and source of the FET is equivalent to a resistor, so the FET used in the circuit usually functions as a voltage-controlled resistor, that is, voltage-controlled current. Specifically, one is to manufacture high-speed electronic switches like BJT, such as induction cookers, and the other is to perform analog control such as amplification.

Specifically, you can read books on analog electronics. Typically used as a high frequency switch to turn circuits on and off. The most common function is to convert direct current to alternating current, but it is not limited to that.

Field effect tube, what does it do?

The FET has the same function as the triode, and it plays an amplifying role, but the input resistance of the FET is much larger than that of the triode, and it is mostly used in the input stage of the amplifier circuit with high input impedance.