Take, for example, the directory at ftp://ftp.xemacs.org/pub/xemacs/. If you retrieve it with -r, it will be saved locally under ftp.xemacs.org/pub/xemacs/. While the -nH option can remove the ftp.xemacs.org/ part, you are still stuck with pub/xemacs. This is where --cut-dirs comes in handy; it makes Wget not “see” number remote directory components. Here are several examples of how --cut-dirs option works.
No options -> ftp.xemacs.org/pub/xemacs/ -nH -> pub/xemacs/ -nH --cut-dirs=1 -> xemacs/ -nH --cut-dirs=2 -> . --cut-dirs=1 -> ftp.xemacs.org/xemacs/ ...
If you just want to get rid of the directory structure, this option is similar to a combination of -nd and -P. However, unlike -nd, --cut-dirs does not lose with subdirectories—for instance, with -nH --cut-dirs=1, a beta/ subdirectory will be placed to xemacs/beta, as one would expect.