This window is opened from the main window's Settings menu.
Generally there's no point selecting any of the logging checkboxes. I used the logging for developing Shaken, not stirred, to check if it was doing what I expected, and left the capability there in case I need it for future updates. If you're curious, go ahead.
When logging options are turned on, files are created each time the shuffle or album art copy runs, with information on the logic used to reach the final result. These are for information only, and have no effect on the final result.
The file most likely to be of interest to users is "Repeats distribution.csv", which opens in spreadsheet programs like Microsoftt Excel or free Open Office Calc. It shows how many times each song was repeated in the playlist before the playlist was truncated. You can use that to see if your shuffle selection is generating the play frequencies you wanted.
The .txt files record the steps taken by the program, and the information in those files doesn't make much sense without referring to the program's source code.