ISO invariance means deliberately underexposing at a particular ISO and then correcting for that underexposure in editing, giving the effect of shooting at the higher ISO in the first place. A camera with good ISO invariance will exhibit little difference between the underexposed shot and the one exposed at the ‘correct’ ISO.
To explain, let’s say you set ISO 100, underexposed by one stop, then brightened that image in editing by one stop; in effect, you have an ISO 200 photo. In Photoshop or Lightroom, the limit for exposure correction is +/-five stops, so if you took a shot at ISO 100 and repeated the process by five stops, that is effectively an ISO 3200 image (-1 ISO 200, -2 ISO 400, -3 ISO 800, -4 ISO 1600 and -5…