NEC 2SK3919 MOSFET replacement
As to Vds and Vgs, those ratings should be the same or higher. As to the on and off times, those should be the same or faster. Gate charge or capacitance should be the same or smaller. ON resistance value should be the same or lower. 

This MOSFET, like most, is also equipped with a body diode. That diode will have a reverse recovery time, and your replacement MOSFET must have a diode with a recovery time that is the same or smaller.

As an aside, for the most part, what this MOSFET is doing for the PSU is acting as the switch in a switching power supply or voltage regulator. Generically, these are used to regulate voltage and current to various components on the board.