A staff meeting was a type of meeting where co-workers discussed business.
In 2368, Ms. Kyle interrupted a staff meeting to ask Worf about setting up placement examinations for his son Alexander. Worf told her it was not a good time and said he'd call her later. (TNG: "New Ground")
Admiral Rollman remarked to Captain Sisko, "That Bajoran woman you have working for you interrupted a staff meeting to tell me how she disapproves of your handling of this asylum matter." (DS9: "Past Prologue")
In 2375, when discussing the senior staff conference room aboard USS Voyager, Captain Janeway remarked "Starfleet's most up to date vessel and they still can't design a comfortable place to hold a meeting." (VOY: "Relativity")
That same year, Sarina Douglas expressed her relief at spending time with Julian Bashir's fellow Deep Space 9 crewmembers rather than her fellow Institute patients. She commented, "I felt so comfortable around them. I didn't have to worry that someone was going to throw a tantrum, or break into tears all of a sudden." Bashir assured her that they only exhibited that behavior during staff meetings. (DS9: "Chrysalis")