To supplement GrandFather's excellent explanation, here is the output generated by YAPE::Regex::Explain. 
use warnings;
use strict;
use YAPE::Regex::Explain;

my $re = 's!(?:^|/)[^\s,@;]*(?<=/)([^\s,@;]+?)(?=[\s,@;]|$)!$1!g';
my $parser = YAPE::Regex::Explain->new($re);
print $parser->explain;

[download]
The regular expression:

(?-imsx:s!(?:^|/)[^\s,@;]*(?<=/)([^\s,@;]+?)(?=[\s,@;]|$)!$1!g)

matches as follows:
  
NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  s!                       's!'
----------------------------------------------------------------------
  (?:                      group, but do not capture:
----------------------------------------------------------------------
    ^                        the beginning of the string
----------------------------------------------------------------------
   |                        OR
----------------------------------------------------------------------
    /                        '/'
----------------------------------------------------------------------
  )                        end of grouping
----------------------------------------------------------------------
  [^\s,@;]*                any character except: whitespace (\n, \r,
                           \t, \f, and " "), ',', '@', ';' (0 or more
                           times (matching the most amount possible))
----------------------------------------------------------------------
  (?<=                     look behind to see if there is:
----------------------------------------------------------------------
    /                        '/'
----------------------------------------------------------------------
  )                        end of look-behind
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    [^\s,@;]+?               any character except: whitespace (\n,
                             \r, \t, \f, and " "), ',', '@', ';' (1
                             or more times (matching the least amount
                             possible))
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  (?=                      look ahead to see if there is:
----------------------------------------------------------------------
    [\s,@;]                  any character of: whitespace (\n, \r,
                             \t, \f, and " "), ',', '@', ';'
----------------------------------------------------------------------
   |                        OR
----------------------------------------------------------------------
    $                        before an optional \n, and the end of
                             the string
----------------------------------------------------------------------
  )                        end of look-ahead
----------------------------------------------------------------------
  !                        '!'
----------------------------------------------------------------------
  $                        before an optional \n, and the end of the
                           string
----------------------------------------------------------------------
  1!g                      '1!g'
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------

[download]

In reply to Re^3: This regular expression has me stumped by toolic
in thread This regular expression has me stumped by tsk1979

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