Packs off allows more engine thrust to be used for the take off. The maximum weight you can take off with is determined by the runway length, obstacle clearance and climb gradient which are all affected by the temperature and pressure (aircraft also have max structural take off weights). If a "Packs On" take off gives you a climb obstacle clearance limit of 55t, you will find that with Packs Off you can take off at 56t because you have a little bit extra thrust.
So the conditions when you will use it is when the aircraft weight, the field limits, or the climb limits mean that you need the extra thrust.
SW