The official record kept by a starship's commanding officer, dictated to the computer and dated by stardate, which opens and narrates most Star Trek episodes.
The captain's log is the formal record of a Starfleet vessel's voyages, spoken aloud by the commanding officer and stored by the ship's computer. Each entry is dated with a stardate, and later additions on the same matter are marked as supplemental. Other officers keep logs of their own, including medical, science and personal logs, and an acting commander records entries in the captain's place.
Kirk's log entries frame nearly every episode of the original series, and the device carries on with Picard, Janeway, Archer, Pike and their successors. On Deep Space 9 the equivalent is the station log kept by Sisko.
Some stories turn on the log itself. Data's Day is told as a letter drawn from Data's personal log, and In the Pale Moonlight is a personal log entry that Sisko erases once he has finished confessing to it.