LOG profile or Logarithmic profile which I believe many cinematographers would know what the meaning is, but in case you’re just starting out as an amateur and you don’t know what it means, I will explain briefly about it.
A log profile is a short form of logarithmic footage. A log is a shooting profile, or gamma curve, found on some digital video cameras that give a wide dynamic and tonal range, allowing more latitude to apply colour and style choices. A log is when your camera shoots in the flattest setting possible to preserve the number of details and dynamic range. This is when the original video looks washed out which later some colour grading in post-production.
There are different log names for each camera and they basically serve the same purpose; S-Log on Sony cameras, C-Log on Canon cameras, F-Log on Fuji cameras, N-Log on Nikon cameras, etc.
This video by Wazas Qazi shares useful ways in which you can use your log from different cameras to get the desired result and also how to convert your logs.