NOT EDITED YET, DIRECT RIP FROM UPDATE (Partially edited, will finish tomorrow)
One way to think about wealth in general is that it represents how many "ducats" worth of property exist in the province. It doesn't represent how many ducats are literally in the province. Let's look at a real life example. If on your personal property you own a house worth $100,000, a car worth $15,000, a computer worth $1,000, and you have $500 stashed under your mattress, then the total "wealth" on your property is $116,500, even though the fluid capital on your property is only $500. Provinces work the same way.
Introduction to Wealth Edit
Wealth is the amount of currency in each province, There are two different kinds of wealth, Asset wealth, and there is fluid wealth. Asset wealth is best represented as non-currency wealth, such as buildings and valuable personal belongings. Fluid wealth on the other hand is wealth stored in currency such as coins, bullion, or gems. When you combine the two, it represents the total ducat value of all the valuables in a province. So for instance, at game start, there is 2,600 ducats worth of wealth In Paris. In theory, this wealth *can* be liquidated into ducats, just like you could sell your computer or your car for money. If you decide to banish all of the Jews in a city and seize their property, what you are doing is seizing the wealth stored up in buildings or which exists as fluid capital. So if half of a city consists of Jews and there is 2000 ducats worth of wealth in the city, then half of that wealth is seized, leaving the province with 1000 ducats worth of wealth. What happens then is 1000 ducats worth of buildings are then destroyed. (building are far more expensive in M&T 2.0)
The same thing occurs when soldiers pillage a city. If you march into Paris, which is worth 4100 ducats, and you pillage 20 percent of the wealth, 820 wealth is subtracted from Paris. 300 of that wealth might go to the invader's treasury as 300 ducats. 300 might go to the troops who looted, most of which would be transferred back to provinces in the invader's country. The remaining 220 would be destroyed (because when you loot stuff, some is damaged and when you firesale it, the value isn't as high as it was back in the place you looted it from). Back in Paris, buildings are destroyed until there is no longer a wealth deficit.
Wealth Growth Edit
So, with that under our belt, how does wealth grow? Well, we've already learned it can be stolen, but that's probably the smallest way that wealth is gained, and it ultimately causes a net decrease in the world at large. Another way is by government intervention. So for instance, if you have 500 ducats in your treasury and you build a 500 ducat building in Florence, 500 ducats leaves your treasury and Florence's wealth goes up by 500. However, the most important way that wealth increases is by economic growth. Every year when population is calculated, new wealth is calculated as well. For each urban population that you have, X amount of wealth is generated multiplied by the value of the economic buildings in the province. So merchant buildings, production buildings, and infrastructure all have a positive influence on wealth. 1 urban population in Marina might only be generating 1 wealth per year, where as an urban pop in Florence might be generating 1.6. Also, centers of trade and centers of production have a positive influence on wealth generation as well. This extra wealth then goes directly into the fluid wealth variable, not assets. As the years tick by, this fluid wealth accumulates. Once there is a big enough pool of fluid wealth, this fluid wealth then gets converted into asset wealth in the form of a new building in the province.
So in theory, you can approach "development" of your country in different ways. You can try to earn as much money as possible and build buildings yourself, or you can try to foster "wealth generation" in your country. So for instance, instead of spamming buildings in your home provinces directly, you might open up trade routes abroad, which empowers your trade centers back home and gives bonus multipliers in those trade centers. Also, these areas can overlap in many ways. So for instance, you could pick the policy "expand infrastructure" which would give you a significant manpower reduction, but would then activate frequent events which would give you the chance to build roads in various provinces at a significant discount (with some of the bill being subtracted from the province's wealth).
At the end of the day, what we end up with is a world that is not only breathing population wise, but a world that is living and breathing economically. Even if you don't build a single building personally in your country, if you take care of it and ward off harmful influences, it will grow on its own.
Oh, and one last thing about wealth... All provinces get a special wealth modifier based on the wealth in the province. This serves multiple purposes. The most important purpose is that the wealth in a province modifies local build costs. For the same reason that its way more expensive--- but way more lucrative--- to start a business in New York City than in some small town, the same is true in the Pop Overhaul. So for example, if Florence's wealth is 2,600, its wealth rank would be 7. This will add some base trade power to the province, but it will also give the province a substantial malus to its local build cost: 140%. In other words, if you want to build a new building in Florence as opposed to Marina who has a wealth rank of 0, it will cost 140 percent more. This might seem punishing, but consider this: Florence is already full of urban dwellers, which means any benefits from that building in Florence will be multiplied by its existing population. Also, any wealth generated by the new building will be multiplied into the existing population as well. In other words, it might cost you 140% more to build a new building in Florence, but the benefits of building that new building is somewhere around 140% more beneficial, though it depends on what exactly you are building.