Tip #9 from the Basic debugging checklist: YAPE::Regex::Explain

The regular expression:

(?-imsx:((.*)EDITION/|Edition/)(.*))

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):
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    (                        group and capture to \2:
----------------------------------------------------------------------
      .*                       any character except \n (0 or more
                               times (matching the most amount
                               possible))
----------------------------------------------------------------------
    )                        end of \2
----------------------------------------------------------------------
    EDITION/                 'EDITION/'
----------------------------------------------------------------------
   |                        OR
----------------------------------------------------------------------
    Edition/                 'Edition/'
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  (                        group and capture to \3:
----------------------------------------------------------------------
    .*                       any character except \n (0 or more times
                             (matching the most amount possible))
----------------------------------------------------------------------
  )                        end of \3
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
[download]

3) In this syntax $1 = ((.*)EDITION\/|Edition\/) and $2 = (.*), so what will be $3 ?

A numbered capture group is numbered according to the strict order in which its opening parenthesis appears in the regex:
   $1 --+-----------------------+
        |                       |
        V                       V
       /((.*)EDITION\/|Edition\/)(.*)/
         ^  ^                    ^  ^
         |  |                    |  |
    $2 --+--+               $3 --+--+
See perlre, and also Grouping things and hierarchical matching and Extracting matches in perlretut.

Alternation is constrained only by grouping parens, or by the pattern as a whole. In your case, you've got two alternates of choice:

(.*)EDITION/
[download]

...or...

Edition/
[download]

Whichever of those alternates matches will be captured into $1. $2 will only be populated if the first alternate is matched, however. $3 will always be populated with something (assuming the overall pattern match is successful), even if that something is an empty string; it takes place outside of the alternation.

The \/ construct equates to the literal forward slash. It has to be escaped with a backslash so that it doesn't get confused with the m// operator's terminating /.

As for your last question: $1 will get everything matched by (.*)EDITION\/|Edition\/. $2 will get everything matched by the first (.*), but only if the first alternate in your alternation is matched. $3 will get everything matched by the final (.*).

What are you actually wanting to match? Is it true that you only want $2 to be populated with a useful value if the text contains EDITION/, but not if it contains Edition/?

Will this regex mean entire path "..." ... ?

Why not just do a few experiments and find out?

>perl -wMstrict -le
"my $v_path = '//rsoesn/main/dis_sites/EDelivery/EDITION/scc_audit0109
+2014';
 print qq{   '$v_path'};
 ;;
 $v_path =~ m/((.*)EDITION\/|Edition\/)(.*)/;
 print qq{\$1 '$1'};
 print qq{\$2 '$2'};
 print qq{\$3 '$3'};
"
   '//rsoesn/main/dis_sites/EDelivery/EDITION/scc_audit01092014'
$1 '//rsoesn/main/dis_sites/EDelivery/EDITION/'
$2 '//rsoesn/main/dis_sites/EDelivery/'
$3 'scc_audit01092014'
[download]