UPDATE 20 September 2016: Note that the info in this article is valid for DP versions 9.0x and earlier. The behavior may be changed in a later version.
The logging level is one of the options which can be set for a backup or object copy or consolidation. See the screen captures for the location in the "Backup" and "Object Operations" GUI context. The logging level determines the volume of detail on files and directories written to the IDB during backup, object copy or object consolidation sessions.
Please note that, as opposed to what you may be expecting, "Log Files" will not allow a fast (single) file restore. When restoring from a backup made with "Log Files", the offsets for seeking to the file are missing. If a fast file restore is desired then the backup should be made with "Log All". This way the offsets will be available and a seek right to the file will be possible.