When the gate-source voltage of a MOSFET exceeds a certain voltage (threshold voltage, |Vth|), the drain-source resistance decreases, causing the MOSFET to turn on. This drain-source resistance is called on-resistance.
The direction of the voltage applied across gate and source differs between n-channel and p-channel MOSFETs. The following figure shows the condition under which a MOSFET turns on.
N-channel MOSFET: When the gate voltage is higher than the source voltage by |Vth|, the n-channel MOSFET turns on.