Hi. I am new to the Total War series, having had only Medieval 2 + Kingdoms for about three months. However, from my experiences, I have decided to write a (not so) mini-guide as a measurement of how much I know.
Rebel Armies:
Overview: These suckers are there from the beginning of the game and don't go away. They don't seem to be doing anything at first glance, but they can and do affect you in many ways.
Public Order: Any rebel army in your region will slightly decrease the public order in that region. So, if you're sitting in (for example) Zaragoza wondering why the public order is in yellow when you have a Governor and all your upkeep slots filled with militia, this may be the reason. Other reasons include foreign spies in your city or a bad Governor. Basically, this is one reason why you want to drive out this rebel army. Keep in mind that city public order is more affected than that of castles.
Experience: How would one drive this rebel army out? By battling them, of course. Rebel armies provide an easy way to earn battle experience, albeit a very small amount. Depending on your battle style, one can completely destroy a rebel army, or just let it rout away. Hopefully, if they rout, they will go to another territory, preferably one not of your faction, but no guarantees. Any units that you capture are instantly executed as you can't really ransom them away to anyone. Keep in mind that the majority of rebel field battles will be fought at the beginning to middle stages of the game, when they are some rebel field armies still around. Notable exceptions are when you have destroyed another faction and that faction's remaining armies turn rebel. Two things can result from battling rebel armies. One, your generals will gain valuable battle experience, or two, if you fight enough battles, your captain will be promoted to a general, and you will have gained a new unit of General's Bodyguard, which is always helpful.
Devastation: If a rebel army is on your territory for too long, they will start to cause devastation. Devastation can actually be seen on the map, any army standing too long in one spot will cause it. Devastation in an enemy faction's territory is beneficial, as their food production and population growth will take a slight downturn. If the same devastation occurs in your territories, the same negative effects will result as well. Hence, another reason to remove these pests from your lands.
Rebel Settlements:
Overview: At the beginning of the game, many settlements surround your faction's cities and castles. The majority of these (in the beginning) will be rebel settlements. They look ripe for the picking, but all may not be as it seems.
Expansion: This is probably the most important aspect of the whole game: expansion. Total War simply would not be Total War without it. Besides, not matter what campaign you play, victory conditions include having either 15 regions or 45 regions, including certain settlements that you don't start with. How does one get to 15 regions or 45 regions? Through expansion, and the expanding you will do at the beginning of the game will be through rebel settlements.
Sounds simple, doesn't it. Take a rebel settlement, upgrade its buildings, create more troops, take more settlements, and sooner or later you will have won the game. At a fundamental standpoint, that is the game. There is so much more complexity to it, of course, but big things start small. (There was a lot of rambling in that, but I'll try to keep it more concise from now on.)
To win, you need territories, and to get territories, you need to fight the garrison within these. The majority of rebel settlements will have a small garrison, but exceptions include Valencia, Bruges, Antwerp, etc. Valencia even has its own general, El Cid the Chivalrous. But aside from these exceptions, most rebel settlements will have maybe three, four, five, maybe six units as a garrison. With five to six units of your own, these rebel settlements should be a piece of cake. (If you have trouble taking rebel settlements, consult the Scriptorium.)
Once you have conquered a rebel settlement, you will have the option to occupy, sack, or exterminate. Depending on what region you have just conquered, and what kind of player you are, you will choose on of these three settlements. Occupy if there is no bonus from sacking, and if you want to increase your general/king's chivalry. Sack if the monetary bonus is worth it; I'm talking a prize of 20,000 to 30,000 florins minimum. Exterminate if you have conquered a region of a different religion without converting its peoples first. Spain and Portugal have this problem many times.
However, once you have selected your option, you will be one step closer to victory, not to mention you will be richer, have the chance to create more units, etc. The more the merrier when it comes to settlements.
Papal Favor: Papal Favor is crucial to the game; having low favor will eventually get you excommunicated, which is basically an invitation for other catholic factions to attack you. If you are playing as a Muslim or Orthodox faction, this does not apply to you. Basically, expanding through rebel settlements will not incur the wrath of the Pope. The Pope does not give a damn if you take rebel settlements, so do it. Take rebel settlements, they're as fundamental to the game as war itself.
Conclusion: Basically, rebels are more important to the game than you may think. They provide experience, they cause negative effects, and they're the perfect way to expand (in the beginning). If you want to win the game, attack rebels. It's as simple as that.
(P.S. I left out some things, and this turned out to be much longer than I had originally anticipated. This is my first guide, however, and I hope you like it.)