A public figure was a person who was known to the general public.
Between 2371 and 2373, Tekeny Ghemor kept an ear out for information on Kira Nerys. According to him, she was a public figure; not only was she the first officer of Deep Space 9, a significant presence in the quadrant, but she had gained some notoriety for her feud with Kai Winn. The Cardassian Central Archives had an entire section on her. Ghemor assured her that she had made a good impression on people and that she should be proud of her work, as he was. (DS9: "Ties of Blood and Water")
After seeing himself quoted in a 2373 Federation News Service article by his son Jake Sisko, Benjamin Sisko noted that now he would see everything he said in print. Jake reminded him that as captain of an important space station, he was news. Benjamin did not like being reminded of that. (DS9: "Call to Arms")