I will begin by saying this: Loyalty is not like Morale from GalCiv 2. I don't know about all of you, but the Morale from GalCiv2 filled me with a sort of hatred that I can't explain entirely.
Loyalty is a new resource. It represents the collective will and belief of all your citizens in your right to rule, your power, and your desire for their survival. Loyalty comes from having citizens who are loyal to you (IE, generated from cities in general) and some structures will increase loyalty production. For example, if every 100 people generated 1 loyalty per turn, a Royal Statue might increase it by 10%.
Each turn, you'll get more added to your Loyalty pool. Hitting zero or going into 'loyalty debt' does nothing except inhibit your ability to use Loyalty.
Loyalty is used as a sort of mana pool. There are various Doctrines, Laws, and Decisions that you can make regarding your kingdom. Laws represent very long term things that you can implement at a Loyalty cost, perhaps with a Loyalty upkeep or other upkeep (gold, etc.). Laws last a certain amount of time and cannot be cancelled until that time is up. Doctrines are like Laws, but toggleable - you can turn them on and off whenever you want, but activating a Doctrine takes Loyalty. Decisions are short term things that, when used properly, can drastically change your situations.
Spending Loyalty nets you many, many benefits. You could spend Loyalty to pass a law that increases gold income for the next 25 turns. Perhaps you are having many issues with your neighbor, so you use Loyalty in a Decision that, while costing a great deal, gets you a massive one-turn gold boost (because you demanded all citizens to hand over X gold, perhaps) and then build up a quick army. Maybe you decide to Draft some of the population of a city into a quick, weak army. You have a new frontier city? Pass a Law that rewards all citizens who move to it, taking 1-2 Prestige from each of your other cities and giving it to the targeted one, with a small (1-2) gold lost per new citizen at that city.
Some other ideas that come to mind…increased taxation doctrine (-material income, +gold income) lessened taxation doctrine (vice versa), required military training law (-1 turn to produce units), mandatory schooling law (+research income, -gold income, +1 military production time), standing army doctrine (-army upkeep, greater loyalty debt), gardening reward doctrine (+food production, -gold income).
Each use of Loyalty imposes a varying amount of reduced Loyalty income, even Loyalty debt. Decisions generally cost the most and have a massive (-50%) loyalty debt because they are the most drastic. Doctrines are of moderate cost and usually incur a small debt (no more than 3 per turn) because of their milder nature. Laws, both because they are the least outrageous and because they cannot be reversed, have a very small Loyalty impact both in terms of debt and in terms of initial spending.
Loyalty is also used passively. As you gain more Loyalty, your cities begin to become affected too, to the point that enemies will have a hard time just running through. If you have a high amount of loyalty and a city is taken, it will naturally suffer a prestige drain (as your people flee from their new masters) and your cities will gain prestige (as they come back to you). Further, upon losing a city, you may spend certain amounts of loyalty to make that captured city harder to hold. For example, your captured city could suffer from Unrest (giving your troops an advantage in a battle to retake the city in the immediate, 5-10 turn future), could suffer from Sabotage (your citizens damage new buildings or destroy them entirely), from Smuggling (the city loses 75% of its income for a period of time, and you gain 25% of that income from Smugglers).
These loyalty effects require high upkeep and will deteriorate after a period of time, based on the loyalty when the city was captured. Perhaps 100 loyalty = 1.1 turns of effects, rounded to the nearest whole number (IE: 500 loyalty gives 6 turns, not 5).
To avoid city spamming, each city you make loses .2 per application. That is, if every 100 citizens gives 1 Loyalty normally, then your second city would give .8 loyalty per 100 citizens, your third will give .6 loyalty, fourth .4 loyalty, fifth .2 loyalty, sixth 0 loyalty, seventh -.2 loyalty…etc. Do note that this only affects cities that you have built – all captured cities give increasing loyalty from -2 to .3 per 100 citizens, which takes as long as the loyalty affects mentioned above.
Loyalty is also partially effected by Diplomatic incidents. For example, if an attacker razes one of my cities, my Loyalty effects are increasingly painful, last twice as long, and cost much less Loyalty to implement.
Thus, we not only have a requirement to keep a strong garrison in a captured city due to Unrest, we also have a period of time where we can’t build safely in that city, due to Sabotage, and that city might take a massive chunk of gold and other resources due to Smuggling. Furthermore, that city is going to drain my Loyalty pretty fast. Gone are the days when we can just roflstomp an enemy.