small signal model of a MOSFET (or a BJT) is taken at a particular bias point and can be used to calculate gain, stability, high frequency response and the loading effects of the transistor in amplifier and oscillator circuits. These are often used to design RF low noise and small signal amplifiers for radio receivers. The simple circuit makes it easy to design oscillators.
This is a fairly simple model for a FET. Vgs is the voltage across the capacitor and the circle with the arrow is a current source whose value depends on the voltage between the gate and the source, Vgs.
The way it works is a relatively small AC voltage is applied between the gate and source and depending on what is connected to the drain you can get a larger voltage on the output.
This circuit demonstrates that at low frequencies the FET input, the gate, looks like an open circuit. This makes FETs ideal for switching things. They use no power to either block or maintain a current path. The only power required is that transferred when charging or discharging the capacitance at the gate during switching.
With a very high impedance circuit on the drain of the device the gain of a FET will have a maximum voltage gain of Gm, the FET transconductance, times the resistance between source and drain in the model, sometimes called Rds. With longer gate FETs this can be 100 or more.