Primarily, the Armageddon counter triggers Armageddon events. these include:
@AC 10: A warning about the AC, but no effect.
@ AC 40: Blight: Destroys all pastures, plantations, farms, camps, and winery improvements in the world; 25% chance to destroy each source of the wheat, corn, rice, deer, cow, pigs, sheep, sugar, and wine; 50% chance to remove each ice feature; 25% chance for each plains tile to turn to desert.
@ AC 60: Stephanos appears in the world. (The first of the Four Horsemen of the Apocalypse, a powerful demonic flying mounted barbarian Hero. He causes fear,and is immune to magic)
@ AC 63: Buboes appears in the world. (The second of the Four Horsemen of the Apocalypse, a powerful demonic flying mounted barbarian Hero. He causes fear, is immune to magic, and can cast Rage)
@ AC 66: Yersinia appears in the world.(The Third of the Four Horsemen of the Apocalypse, a powerful demonic flying mounted barbarian Hero. He causes fear, is immune to magic, and spreads the Plague)
@ AC 69: Ars Moriendi appears in the world.(The fourth of the Four Horsemen of the Apocalypse, a powerful demonic flying mounted barbarian Hero. He causes fear, is immune to magic, and All (living?) units he defeats are turned to barbarian Wraiths, like the Death III summon but with unlimited duration)
@ AC 70: Hellfire: This creates the Hellfire improvement on random tiles in the world, and creates a Sect of the Flies (a demonic melee unit) (belonging to the Infernals if they are in the game, and to the barbarian state otherwise) on these tiles to defend them. More such units (and even stronger demons) will continue to spawn here if the AC remains high enough.
@ AC 90: Wrath: The Avatar of Wrath appears in the world. He is a powerful Barbarian Hero that can walk on water and can cast fireball, and units he defeats join the barbarian state. This event has a 60% chance of giving each unit in the game (except world units, so you won't lose heroes) the Enraged promotion. This promotion gives them a chance to turn barbarian each turn (note that whenever you disband a unit with a chance to turn barbarian, it will instantly turn barbarian instead of being deleted)
@ AC 100: Apocalypse: kills 60% of the living units in the world, and halves the populations of all cities of leader without the Fallow trait (anyone but Hyborem)
There are also several negative random events that require certain minimum ACs, but they are nothing compared to these ones, which always happen the first turn when the AC ht the prerequisite AC.
Also, The Stigmata Promotion gives a combat bonus of (AC/2)%. This promotion is available to Demons and the Undead with combat 5, and free for all units created in the City with the Stigmata on the unborn (the Ashen Veil Shrine)
The AC effects diplomacy. The Diplomatic penalties (but not the bonuses) between the different alignments scales based on the AC, and civs become more aggressive. Also, the largest contributer to the AC gets a significant diplomatic penalty with all civs without the Ashen Veil Sate religion, and the same size bonus to those with it. (I think there may also be a similar bonus for whoever lowers the AC the most with non AC civs, and a similar penalty with AC civs)
Edit: there actually were a couple of things I forgot to mention.
If you are playing as the Sheaim (or against them), you'll probably want to know that your Planar Gates depend on the AC. For each city the Sheaim have with a planar gate that also has certain other buildings they have a chance of getting a free unit in each city each turn, up to a certain limit. It looks like the maximum number of free units of each type that you can have at a time is equal to the number of Planar gates you have while the AC is less than 50, is double the number of gates between AC 50 and AC 75, triple the number of gates over AC 75, and quadruple the number of Gates at AC 100. The AC also effects the chances of getting free units in each city each turn. It looks like from AC 0 to AC 50 there is a 600 (found in the global defines.The other rates are multiples of this define) in 10 000 chance, from AC 50 to AC 75 a 900 in 10 000 chance, from AC 75 to AC 99 a 1200 in 10 000 chance, and at AC 100 a 1500 in 10 000 chance of getting of getting a free unit in each city each turn. The free unit is randomly chosen from among the units allowed by the buildings present in the city, so long as you don't have too many of those units yet. If the city that would provide the unit does not have a building that allows a unit of which you don't have too many, then you get nothing.
The Buildings needed for Planar Gates units are:
Gambling Houses for Revelers, a recon unit that can see invisible;
Mage Guilds for Mobius Witches, essentially free mages that start at level 4 with a chance to start with any first level sphere promotion (except that Shadow and Sun have not been added to this list), and can upgrade to Archmages, letting all your adepts aspire to become conjurers, and eventually Eaters of Dreams (Summoner UU, has an ability that consumes 1 city pop in order to regain the ability to cast again. Combined with the Summoning Trait, this makes Armies of Sheaim summons very potent);
Carnivals for Choas Marauders, the same melee unit as the Chaos II summon but without the chance to turn barbarian (remember these get metal weapons promotions if you have the resource);
Large Animal Stables for Manticores, quick and powerful demonic "mounted" units;
Public Baths for Succubi, a demonic melee unit that does unholy damage, can use metal weapons, can cast charm, and is the first topless female unit in the game;
Weapons Smiths for Minotaurs, melee units with high defensive strength; and
Temples of the Veil for Tar Demons, a demonic disciple class blob of tar with high defensive strength that used to be a lot cooler back when it would split into 2 weaker tar demons upon defeat (which would gradually increase to the original strength. the weakest ones couldn't split), but isn't as great anymore
It also seems I forgot to mention Hell terrain. Whether an individual tile is in hell or not depends on that tile's plot counter (which is different than the AC. If the plot counter is over 10, then it is hell. Most tiles change to a different "Hellish" terrain at this point, and change back when th counter dips below 10 (I think it used to be 20, but the code clearly says 10 now). There are some terrains, like tundras and water, that currently have no different version for hell.
Each tile is updated once per turn. All tiles owned by the Infernals have their plot counters set to 100. (I was also under the impression that Mercurian lands had their counters always set to 0, but since I don't find any mention to them in this code and since I've often had to wait for hell to recede from my lands when playing as the Mercurians, I assume this has been changed.) Any tile belonging to an Ashen Veil civ regardless of the AC, to any Evil civ at an AC of 25 or greater, or any Neutral civ at an AC of 75 or greater that borders a tile with an plot counter of at least 10 will have its plot counter increased by one each turn. (Good Civs are never effected, much to my chagrin.) Unowned tiles likewise have their plot counter increased by 1 each turn if they border a tile with a counter of 10+, if the AC is at least 25 (I could have sworn that non-AV evil lands turned to hell before unowned lands, but thats not what the code seems to say.) Tiles with positive plot counters that haven't been increased will have theirs decreased.
Note that while changing the plot counter immediately changes the terrain (e.g., the sanctify spell sets the plot counter of the surrounding tiles to 0, and immediately reclaims the hell terrain, temporarily), the resources aren't updated but once per turn. Also note that since several Hell resources are replacements for multiple normal resources, they won't necessarily revert to the same resource they were before hell spread to the tile. (e.g., Hell's spread could turn your horses to Nightmares, which then may revert to cows when hell is pushed back.