It's been a while since I played, however personal wealth is tied to the government posts that character holds. Plus some traits as well as events influence the rate at which wealth is generated. Wealth is passed along to children on character death if I recall correctly, and to the government in the case of character death with no living inheritor. Banishing and executing people will result in character wealth being confiscated by the government. (Except in execution if the character has a living inheritor)
Character wealth is measured differently then national wealth at a rate of 100 = 1. (Where the 100 is character wealth, and the 1 is national wealth).
Some events for characters can only fire if the character is at a certain wealth amount. Both positive and negative events can occur this way.
Unit loyalty to a general causes that general a extra cost per loyal unit, this is removed from their personal wealth. (I think this right anyways)
I believe this information is all correct, but I haven't played in a while. Hopefully someone more active can corroborate and provide more detailed information. I will strike any information mentioned to be wrong.