A "troublesome mind" is a member of the telepathic Isitri species whose telepathy is far stronger than that of the average Isitri.
These troublesome minds appear every few generations and are unable to be controlled as they push their thoughts and emotions upon other Isitri. This leads to the "troublesome mind" being able to control all of the Isitri since they're interconnected telepathically.
On occasion these minds decide to fight wars against the Isitri's interstellar neighbors, the Odib. These wars were extremely bloody for both sides and led the Odib to impose a treaty upon the Isitri that says they must be notified of any "troublesome minds" and that if the Isitri don't take care of them the Odib will destroy the entire planet.
In 2270, it was discovered that Berlis Aknista was a "troublesome mind" and the Isitri Council tried to have him killed, but the USS Enterprise intervened nearly leading to a war. Fortunately, the Enterprise's crew was able to stop Berlis and save the Isitri. (TOS novel: Troublesome Minds)