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The term FET is an umbrella term for different kinds of devices, whose behavior is based on the field effect, i.e. the ability of an electric field to control the flow of charges in an internal structure called channel.
FETs are usually 3-terminal semiconductor devices (although there are some exceptions regarding MOSFETs).
Their terminals are called Source (S), Drain (D) and Gate (G). Roughly speaking, source and drain are the "output" terminals, whereas the gate is the "input" terminal.
They come in two variety, named N-channel and P-channel, depending on the polarity of the channel doping, which can be either N-type or P-type.
The channel internally connects source and drain, whereas the gate is connected in such a way that a voltage applied between gate and source will generate an electric field that will influence the conductivity of the channel.
Therefore the basic behavior is that the current flowing through drain and source (IDS) is controlled by the voltage across gate and source (VGS).
FETs are most commonly used as amplifiers and electronically-controlled switches and resistors.