Characters are the most important part of Crusader Kings II, and what sets it apart from other grand strategy games. Everything in the game revolves around the characters, and they're the cause of most of what happens in the game. Every character is an unique person, consisting of a variety of attributes and traits, and belonging to a religion and culture. Most characters are a part of a dynasty, which further shapes their interaction.
Characters come in three types: nobles, burghers, and clergy. This determines the types of holdings they prefer, and is the basis for their relations with other characters.Characters can do a variety of things, everything from participating in plots, to getting married, to pushing their claims on titles, and participating in war.
There are three types of characters, and they interact with other characters in different ways.
Nobles are the most important characters in the Medieval world, as most power is concentrated around them. They are also the only playable characters in the game unless using 'The Republic' DLC.
Nobles come in a lot of varieties, everything from powerless barons, to emperors ruling supreme. They're the driving force of the game, being the aggressors in most wars, and often pushing claims on other nobles. They're the most likely to come from well-established dynasties.
The burghers are the rulers of cities. They're seldom part of a well-established dynasty. Few burghers have any sizable power, but there are a few exceptions, for example the Republics of Venice and Genoa. Burghers can hold titles on any tier, but usually they only hold a single barony.
Burghers are responsible for a large part of the world's economy, as they control the largest source of money in the game, the cities. Beyond that however they usually don't have much of an effect upon the world, as unlike nobles they don't push claims, and are relatively isolationist. Even the clergy affect the world more directly than the burghers, as they're often sizable secular powers as well.
The clergy are the religious rulers. Usually they'll only control a single bishopric, but there are also many powerful members of the clergy, most notably the Pope.
Clergy will pay tax to their secular ruler only if they prefer him over their religious leader. Otherwise, all their taxes will go there instead. As such, it can be very important to keep your clergy happy if you are to become rich. While they won't often push claims, they're much more prone to do so than burghers, as they sometimes come from established dynasties, like nobles.
You might at some point want to change the character type ruling a province, since if they're clergy or a burgher they'll get a permanent -30 to relations with you. Changing the capital of a county and thus the character type ruling it isn't very intuitive, but can be done relatively simply.
All you have to do is gain the county title in some way, for example via revocation or assassination. You then give the title to a noble that owns a castle in the county. His castle will then become the capital of the county while the temple will become a secondary title which he'll most likely delegate to someone else.
It is also possible to change a character's type directly but there is seldom much point. However, if you desire to do so all you need to do is ensure they hold a barony of the target type, then revoke all their other titles. Once they only hold a single barony, they'll become the same character type as the barony.