After you use 'Lookup' to find the album in the database:
you can inspect the items in the Right-hand section and see that they have the correct metadata (Track titles AND Album title).
Pull down the "Options" menu to make sure that both 'Rename Files' and 'Move Files' are enabled.

- Open the app settings (Preferences) and look under
File Naming. You should see that Move Files When Saving and Rename Files When Saving are turned ON.

- Press
Edit file renaming script... to check the file renaming pattern, or select 'Preset 1'. Make sure your file renaming pattern (script) looks something like
%album%/%tracknumber%-%title%
with a Slash (/) character to cause a subfolder to be created. Your operating system might need a backslash (\) character instead.
There are much better and fancier renaming patterns than the above example, like the "Preset 1" pattern below. You can see it uses the slash character as a directory separator:
$if2(%albumartist%,%artist%)/
$if(%albumartist%,%album%/,)
$if($gt(%totaldiscs%,1),$if($gt(%totaldiscs%,9),$num(%discnumber%,2),%discnumber%)-,)$if($and(%albumartist%,%tracknumber%),$num(%tracknumber%,2) ,)$if(%_multiartist%,%artist% - ,)%title%
Screenshots and command names are taken from MusicBrainz Picard 2.8/2.9, but other versions should be similar.