A navigational log was a log of a starship's prior locations, movements and trajectories.
In 2153, after boarding a Xindi-Primate starship, the crew of the Enterprise NX-01 found that most of the ship's computer core – including its navigational logs – had been erased. (ENT: "Stratagem")
In 2373, the crew of the USS Defiant downloaded the navigational logs from a prior run into the ship's auto-pilot in an effort to exactly duplicate the ship's previous trajectory and travel back in time. (DS9: "Children of Time")