Nobles are dwarves appointed to office and rule over your fortress. They provide a critical happiness bonus to unhappy and stressed dwarves, who yell at or cry on the nobles. This provides a safety valve for your most stressed dwarves. They also are responsible for interacting with outpost liaisons.
Nobles enable certain actions and screens
However, some of them can make demands and set mandates which if not met will upset the noble and result in random punishments of your dwarves. They also are aware of their status and do not want a lesser dwarf to have a better room.
It is possible for some of your dwarves to hold noble titles over other parts of the kingdom. These dwarves are still capable of issuing mandates in your fort, however, and demand the same sort of privileged treatment as any other noble.
Appointed nobles are chosen by the player. There are certain social skills that are relevant for each appointed noble's job, and not all dwarves will gain experience in a given skill. In fact, some dwarves will never gain experience in certain skills. This is determined by each dwarf's personal traits, and it is therefore important to select the dwarf with the appropriate set of traits for each position
Appointed nobles: Manager, Bookkeeper