It explains the \U, \L, \u, \l modifiers quite clearly and succinctly!
Its essence is the following:
There are times that you might like to go through a file and change the case of characters that match some arbitrary criteria. If you understand regular expressions well, you can actually do this fairly easily.
It's as simple as placing \U or \L in front of backreferences which you want to change the case of, and \E at the end. Vim will make the text in the backreference uppercase or lowercase (respectively). Use \u and \l (without the \E at the end) to just change the case of the very first character in the backreference.
(A "backreference" is a part of a regular expression that refers to a previous part of a regular expression. The most common backreferences are &, \1, \2, \3, ... , \9).
Some examples that demonstrate the power of this technique:
Lowercase the entire file
(& is a handy backreference that refers to the complete text of the match.)
Uppercase all words that are preceded by a < (i.e. opening HTML tag names):
Note also the gu and gU commands.
For example, ggguG will lowercase the entire file.
(gg = go to top, gu = lowercase, G = go to EOF).
By using the \0 general backref instead of the name ones (\1, \2 etc) you can save some typing for on replace stanza of the regex.
This regex upper cases an explicit set of words to uppercase in a file:
Not rocket science, but otherwise you'd have to do this: