Apparently Mountainhome is happy with my colony, so I got to appoint a baronness, and chose my legendary miner. Now she spends most of her time doing the activity "Noble" in her room. What's that? Should I avoid appointing important dwarves to high positions?
As the Wiki says:
Nobles are snotty good-for-nothing parasites
Jokes aside, noble dwarf are quite demanding, but they are useful because they unlock the possibility to appoint other nobles.
Your baroness, as you can see in the table in the link, will let you appoint Champions and Dungeon Masters (and Tax Collectors in the future)
Being "Noble" means they are doing their own thing. They might be doing nothing, or they might go forge themselves some items and then go tame some monsters (dungeonmaster in older versions of dwarf fortress, for instance).
You cannot give them jobs or tasks, just like you can't give children jobs or tasks (through the game interface, at least). And like children, they will do whatever they want.