(covers information from several alternate timelines)
A voiceprint was an electronically recorded representation of a voice in graphical format. Each voiceprint was unique to the individual speaker. They could sometimes be imitated by voice duplicators, but strong software could detect the deception.
They were commonly used security methods to identify individuals when accessing critical or secured information, including on turbolifts. They had (for the most part) replaced retinal scans between the 21st and 24th centuries.
In 2266, Kirk suspected Anton Karidian of being Kodos, something that a voiceprint suggested was possible, but Kirk was unwilling to convict someone on something that was only "close". (TOS: "The Conscience of the King")
In 2370, Miles O'Brien's voice was recorded by Raymond Boone, a surgically altered Cardassian spy, and was used to create a fake voiceprint to access a weapons locker aboard Deep Space 9, to steal photon torpedoes. (DS9: "Tribunal")
In 2371, Quark accessed Deep Space 9's computer systems to download Kira Nerys' voiceprint, along with her retinal scan and psychological profile, in order to put together a holographic version of her for Tiron. (DS9: "Meridian")
Later that year, on Voyager's holodeck, the computer denied Tuvok from belaying the self-destruct command because his voiceprint was not recognized, due to the fact Seska had locked the holodeck systems. (VOY: "Worst Case Scenario")