A MOSFET is a semiconductor device that can be used as an electronic switch or an amplifier. Some of its critical parts are the gate, source, drain, substrate and oxide insulator. Consider an n-channel enhancement mode MOSFET. This is off when no voltage is applied on the gate. When a sufficient possitive voltage (Vgs > Vth) is applied to the gate then a channel (of electrons) is formed underneath the oxide insulator connecting the source and the drain, allowing current (electrons) to flow from source to drain (if a voltage is applied to the drain/source - Vds). Then the MOSFET conducts current and therefore it can behave as an closed switch. When no voltage or negative voltage (for the case of n-channel enh. mode) is applied to the gate then the MOSFET conducts no current and the MOSFET behaves as an open switch.
Diagram can also be used for illustration