it's a bit confusing,

Some stop growing right in the middle of a level and there is no warning to that effect. You have to keep an eye on it.

Hopefully somebody can answer us.

From memory, you get a certain amount of food per grain. So in other words if you get 50 food per grain and it's a 2 grain city then you get 100 food. 100 food can support 100 population. If you hit 100 population then that city will stop growing.

Some city improvements give you bonuses to food. So if you built an improvement that gave you +25% food per grain, that would mean that your 2 grain city would now produce 62.5 food per grain, or 125 total (I think the fractions are added as you'd expect). Your city will now grow to a maximum size of 125.

There are a limit to the number of food increasing improvements you can build in a city; Towns get quite a lot more, so can generally grow larger and faster. Some Town improvements increase global food production. So if a Town builds an improvement which increases global food production by +5 per grain, your 2 grain city would now be able to grow to 135. There is a spell which will increase the grain of your city by 1, as well, can't remember what it is off the top of my head.

Growth is determined by a few different things, but one of the biggest factors is the difference between your current population and your maximum population. In other words, if your current population is 25 and your total food is 500, then your city could support 20 times more population than it currently has, and it will get +3 growth (which is the amount it grows in population each turn). Again, from memory, I think you get +1 for having up to double the food your current population needs, +2 for up to treble the food your current population needs, and +3 for more than treble the food your population needs. So in the example above with 135 food, you'd have +3 growth up to 45 population, +2 growth up to 67 population, and +1 growth up to 135 population (when it would go to +0). Something like that, anyway. 

There are various buildings and spells which will alter your growth rate. Getting your capital to upgrade from a village as fast as possible is a valid strategy.

So can anyone math up some pratical examples?

Like if you have a 3 grain town how many wells, inns, granaries and other things do you need to make for it to be able to reach level 4?  From that city alone and/or along with other Towns affecting faction per grain?  Practical examples?

I'm getting a headache, where's the cake?

A practical example isn't really practical, imho. I usually try to reach lvl 2 quickly with new cities, after that, I check if I can make a next level easily, otherwise I build more Pioneers. Population by itself doesn't do anything (as Korn469 said). You can check the big progression bar to see how much population you have, and if you can reach the next level or will need to build a food building.

Anyway, in your example, you need to multiply all 'per grain' buildings and techs with 3, since you have 3 grain. This means you need x100 food. You start with 25 (again, all per grain), so you need 75 more. The first 3 buildings add +50 grain. In total, as the bonuses you see next to their techs are not cumulative. Let's say you have already built these, for a total potential population of 225. How can you get this to 300 for a level 4 city?

- Town buildings that increase food p/g in every city. If you already have 5 towns with at least the first building in the 'food for everybody'-line, you are good to go. The first building, Grocer, gives 5 food p/g to all your cities. 5x5 = 25 (*3 grain) + 225 = 300

- If the city is a town, you can build 'food multipliers', like the well. 225x1.5 = 337.5

- City Enchantments: one enchantment multiplies your food, multiplier depending on Essence. The other, early tech one, adds +1 grain to the city. So in the example, it would be 75*(3+1) = 300

Mind you, I have only talked about max population. Growth is something else. I think Merlinme's figures are correct, but there's even more to it...

Man I'm kinda getting it.  I appreciate the attempts @Fallenchar.  It's tough to grasp the intracasies of the additions and multiplications going on here.  Definite see the outlines of the Algebra going on ((umm food , growth) * city bonuses) * or + faction bonuses) or something.

It's situational, but usually, I'd take the 3/3/3 over the 4/3/2

One of the slight quirks of the game is that if you lose population you do not go down city levels. So if you get your city to level 5, it will stay level 5, even if you Sacrifice it down to 10 population. Later in the game when you have a few cities it generally makes sense to have one or two focus on building pioneers (and using Sacrifice, if you have it). I either choose a level 5 town or a town which has reached its highest expected level for the foreseeable future. Playing on higher difficulty levels, cities you've captured off the AI are great for this, as they tend to be very high population. At the point when I can turn 500 population into mana using Sacrifice I generally think I'm well on the way to winning. You can cast Sacrifice multiple times a turn on the same city, so the fact its only half the population at a time is not really a limit. A good city to choose for this is a Town with high growth; with Slums (for example) it's pretty easy to get +6 population growth a turn, and with Sacrifice that is effectively +6 mana a turn. That's on top of the initial bonus of hundreds of mana when you Sacrificed the city's original population.

I've got a city to level 5 a few times, generally by capturing an AI level 4 Town which has Slums. I didn't until I started playing on Ridiculous with the improved AI though, I agree it's not really necessary to win, and certainly not something I particularly aim for.

3/3/3 always. You get that grain back from Sorcery tech (Nature's Grain or something) at the cost of the extra essence, and more essences boost Gentle Rain and Arcane Forge later on, not to mention troop enchants. 

Use Consulates (outpost upgrade), with that and Gentle Rain getting a level 5 city is easy. (+1 Grain and 25% food per essence) The main problem is production to get there since both consulates and food buildings gets expensive, so Enchanted Hammers, Clay pits etc. are very useful for getting cities up fast. 

Conquering the map is a very different thing to do depending on difficulty. I could probably conquer the map without anything but my Sovereign and starting troops on the easiest difficulty.