On set, depending on the size of crew, part of the job for an AC or 1st AC is to make a camera report. Each shot is logged to note things like which lens was used, what filters were used, the height of the camera from the floor, the distance of the film plane to the focus point, the frame rate, aperture, ISO, etc. All of this info can then be used if they needed to do a pick up later to put the camera in the same setup. Also, it can be used in post production so that the camera can be recreated in 3D to have the special f/x match.
Also, log can refer to the gamma curve which affects how roll-offs in highlights/shadows are saved (rough description).
"Log" is still used daily in production work.