Changing the channel width modifies the gain of the transistor. That gain is the base to decide how current flows trhought the NMOS or PMOS transistor. As less width as less current. (W/L).
The area of the MOS transistor under the thin oxide is rectangular with one side as L which is the channel length of the transistor and the other side is W(width),if u want to learn more about the MOS transistor u can read chapter 2 in Design of analog integrated circuits by Razavi
Basically the wider the width of MOS more current will pass through MOS on the other hand there is an increase in parasatic capacitance.
If you say if an NMOS with width x take t psec to discharge a load capacitance then a NMOS with width xx>x will take tt<t psec to discharge the same load capcitance