I think one of the more useful things that most people can get out of this feature, is how they organize their digital media, for instance, songs from iTunes or photos from Picassa. These programs (and others) are good at creating deep structured directory trees for categorizing your individual songs or photos, sometimes with only one file contained beneath a big nest of folders. Eg, %artist%\%year%\%album%\... or \%year%\%month%\%date%\.
With Advanced Move or Copy, you can rename all of your files to contain the folder names inside the filename instead, thus flattening the directory tree. For example.
All your selected file paths and names look like this: M:\iTunes\The Beatles\1968\White Album Disc 1\13 Rocky Raccoon.m4a
You can flatten all that information into the filename thus eliminating the folders entirely.
Old Format: M:\iTunes\%1\%2\%3\%4 %5.m4a
%1 = artist, %2 = year, %3 = album, %4 = track#, %5 = title.
New Format: M:\Flattened\%1 - %3 $(%2$) %4 - %5.m4a
$( = ( and $) = )
Now all your files look like this: M:\Flattened\The Beatles - White Album Disc 1 (1968) 13 - Rocky Raccoon.m4a
It doesn't take much imagination how you can rename all the discs from White Album Disc 1, 2 and 3 to move those numbers into the track number, ie, The Beatles - White Album (1968) 1-13 - Rocky Raccoon.m4a.