Magnetic Variation varies SIGNIFICANTLY near the North and South Poles within a short distance. The Variation Table is a data set containing variation information for geoid positions. The limited range of that table basically applies variation to compass headings to produce true headings and therefore reliable NAV data. Due to minor variation differences nearer the equator and sub-tropics, it can be pretty vague and therefore small in size so takes up less RAM in the archaic A320 FMGC. The A320 wasn't really designed to operate trans-polar, so this wasn't an important feature. In the A330, which came a few years later, RAM had come down in price and due to the nature of long-haul, it would be assumed that trans-polar routes would be planned, therefore it has a better variation table.
I didn't realise that it would cause the AP/FD to trip off without the mod, as compressor stall said, but obviously that makes sense as the FMGC is basically saying the NAV data is unreliable. I assume then the 'Polar Mod' is either a RAM upgrade, or simply a better optimisation of the FMGC data, eg less airports/routes/waypoints filling up the RAM to enable a larger VAR Table? Additionally, I assume this is why autoland is prohibited in certain airports with specific FMGCs. On my fleet, autoland is prohibited in odd places like Johannesburg or Keflavik as the autoland system would presumably align itself in the flare with whatever was tuned as the ILS CRS (a rapidly varying magnetic heading). I haven't tried it but i'm told it aligns itself with the CRS during FLARE so if you were to put a wrong figure into the RAD NAV page, you'd end up with a pretty awful landing, hence the reason we check the CRS during the LAND FMA.