A VIP, short for "very important person", was any individual deemed of particular note. Synonymous terms included dignitary, eminent guest, and guest of honor.
In 2153, Travis Mayweather was surprised that his quarters aboard the ECS Horizon were available for his visit, as they had been re-assigned following his prior departure. Rianna Mayweather explained that the current occupant didn't mind letting him use it temporarily, as they didn't get VIP visitors often. (ENT: "Horizon")
In 2161, Malcolm Reed asked Travis if he was certain their seats at the signing of the Charter of the United Federation of Planets were the correct ones, as he felt they didn't seem like VIP seats. Hoshi Sato suggested Jonathan Archer wanted them to have a fuller view of the event than front seats would have provided. (ENT: "These Are the Voyages...")
In 2365, a shuttle pilot transporting Lwaxana Troi to USS Enterprise-D described her as a VIP passenger. (TNG: "Manhunt")
In 2369, Benjamin Sisko recalled to Julian Bashir how Curzon Dax used to take "perverse pleasure" in assigning Sisko to look after VIP guests. Bashir, assigned to entertain visiting ambassadors, surmised Sisko found similar joy in foisting them on Bashir. The doctor asked Sisko when he stopped being assigned such tasks, to which Sisko replied that it was when he struck one of the guests. (DS9: "The Forsaken")