What do dignitaries do actually?

From my understanding, they help out the local population in assimilating your culture, really helpful after you've conquered a province. But what else?

Every time I click on the stand idle button of a dignitary while he's in my province, my income for next turn goes either up, or down. Typically, I should do it once every 2-3 turns, because every turn would eventually lead to a drop in income.

Sooo, what do they actually do? What are the mechanics of a dignitary?