A confession was a formal admission of criminal or moral guilt. The term could also refer to an honest admission of a fact that was not known previously by another.
In 2269, while Christine Chapel recorded Harcourt Mudd's confession, Spock asked her if he could help her do so. She declined angrily. (TAS: "Mudd's Passion")
In 2293, Leonard McCoy informed the attendees at the Khitomer Conference they had a full confession from Valeris implicating herself and Fleet admiral Cartwright, among others, for the murder of Chancellor Gorkon. (Star Trek VI: The Undiscovered Country)
In 2364, a faked log ostensibly recorded by Jean-Luc Picard during his time on the USS Stargazer claimed to be Picard's confession to mistaken actions. (TNG: "The Battle")