Thank you for cleaning that up. The code:

#!/usr/bin/perl
use strict;
use warnings;
use YAPE::Regex::Explain;

my $re = qr/(%TABLE{.*?name\=\"History[^"]*"[^}]*}%\s*(\|[^\|]*){3}\|\
+s)((\|[^\|]*){3}\|\s)*/o;

print YAPE::Regex::Explain->new($re)->explain();
[download]

outputs

The regular expression:

(?-imsx:(%TABLE{.*?name="History[^"]*"[^}]*}%\s*(\|[^\|]*){3}\|\s)((\|
+[^\|]*){3}\|\s)*)

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:
----------------------------------------------------------------------
    %TABLE{                  '%TABLE{'
----------------------------------------------------------------------
    .*?                      any character except \n (0 or more times
                             (matching the least amount possible))
----------------------------------------------------------------------
    name="History            'name="History'
----------------------------------------------------------------------
    [^"]*                    any character except: '"' (0 or more
                             times (matching the most amount
                             possible))
----------------------------------------------------------------------
    "                        '"'
----------------------------------------------------------------------
    [^}]*                    any character except: '}' (0 or more
                             times (matching the most amount
                             possible))
----------------------------------------------------------------------
    }%                       '}%'
----------------------------------------------------------------------
    \s*                      whitespace (\n, \r, \t, \f, and " ") (0
                             or more times (matching the most amount
                             possible))
----------------------------------------------------------------------
    (                        group and capture to \2 (3 times):
----------------------------------------------------------------------
      \|                       '|'
----------------------------------------------------------------------
      [^\|]*                   any character except: '\|' (0 or more
                               times (matching the most amount
                               possible))
----------------------------------------------------------------------
    ){3}                     end of \2 (NOTE: because you are using a
                             quantifier on this capture, only the
                             LAST repetition of the captured pattern
                             will be stored in \2)
----------------------------------------------------------------------
    \|                       '|'
----------------------------------------------------------------------
    \s                       whitespace (\n, \r, \t, \f, and " ")
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  (                        group and capture to \3 (0 or more times
                           (matching the most amount possible)):
----------------------------------------------------------------------
    (                        group and capture to \4 (3 times):
----------------------------------------------------------------------
      \|                       '|'
----------------------------------------------------------------------
      [^\|]*                   any character except: '\|' (0 or more
                               times (matching the most amount
                               possible))
----------------------------------------------------------------------
    ){3}                     end of \4 (NOTE: because you are using a
                             quantifier on this capture, only the
                             LAST repetition of the captured pattern
                             will be stored in \4)
----------------------------------------------------------------------
    \|                       '|'
----------------------------------------------------------------------
    \s                       whitespace (\n, \r, \t, \f, and " ")
----------------------------------------------------------------------
  )*                       end of \3 (NOTE: because you are using a
                           quantifier on this capture, only the LAST
                           repetition of the captured pattern will be
                           stored in \3)
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
[download]

The match and the substitution have identical bodies, so they will match the same thing. Let us know if the above is unclear.

As JavaFan points out below, you should likely omit the o and e modifiers. bart and AnomalousMonk's discussion below is also very useful - You can likely have wholly equivalent behavior in your code while having only one instance of this long and fragile regex.