IME what this often means has something to do with sound pressure.
That's certainly the potential of a scaled-up sub system (i.e.: added SPL capacity through bigger air radiation area/higher sensitivity/ability to take more power and larger overall size), yes, but it's not the goal per se or rather as much as that which relates to added headroom; performance gains at a similar SPL compared to a smaller/less powerful system due to less cone movement and wattage put through the voice coils, and therefore less distortion and cleaner bass. That's the prevailing logic of (more) headroom, and it's far overlooked in audiophilia in general as large size (and very high SPL capabilities) are usually scoffed at, otherwise deemed undesirable (i.e.: WAF, interior decoration) or ridiculed for being overkill.