Dear
MOI about an axix is the decidin factor for the angular acceleration for a torque about that axix only.
It simply represents the mass distribution quantitavly
so while forming torque equations first choose an axix about which you need to write the equations you can chose any axix but chosing axix about the COM simplifies the problem toa good extent so in this you also rquire to find the MOI about the COM only
Some time you need to arite equation about an axix paralell to the axix passing through the COM in that case you need to use paralell axix theorem
Let me know for further clarification