A symposium, or seminar, was an academic conference. The Annual Starfleet Symposium was an example of this.
In 2293, before the Camp Khitomer crisis, Nyota Uhura was supposed to be chairing a seminar at Starfleet Academy. (Star Trek VI: The Undiscovered Country)
Beverly Crusher met Jas Holza a few years prior to 2368 at a symposium. They danced together at a reception after the symposium. According to Ro Laren, Holza was invited to symposia and diplomatic soirées, but was without real influence among the Bajorans. (TNG: "Ensign Ro")
In 2366, the Astrophysics Center on Icor IX held a symposium on rogue star clusters, which Jean-Luc Picard considered to attend. (TNG: "Captain's Holiday")
The Federation Archaeology Council held an annual symposium. In 2367, this symposium was held aboard the USS Enterprise-D in orbit of Tagus III. (TNG: "Qpid")
During the Psychological conference in 2369, Geordi La Forge attended a warp energy symposium, where he was able to touch a plasma field. (TNG: "Timescape")
In 2371, the senior staff of the space station Deep Space 9 traveled to Earth in order to attend the annual symposium on the current situation in the Gamma Quadrant. (DS9: "Past Tense, Part I")
In 2373 Keiko O'Brien had a botanical pathology seminar on Deep Space 9. This was an excuse for not being able to accompany Kira Nerys, who was then pregnant with Keiko and Miles' baby, to Musilla Province on Bajor. (DS9: "Looking for par'Mach in All the Wrong Places")
In 2377, the Ovions asked The Doctor to speak at a symposium about spaceborne pathogens. (VOY: "Flesh and Blood")
In 2378, The Doctor and Kathryn Janeway attended a medical symposium together. (VOY: "Renaissance Man")