An explanation (beware possible line wrap of intial print of long regex expression):

c:\@Work\Perl\monks>perl -wMstrict -le
"use Regexp::Common qw(RE_num_real);
 use YAPE::Regex::Explain;
 ;;
 print YAPE::Regex::Explain->new(RE_num_real(-keep, -group=>3, -sep=>'
+,', -base=>2))->explain;
"
The regular expression:

(?-imsx:((?i)([+-]?)((?=[.]?[0123456789])([0123456789]*)(?:([.])([0123
+456789]{0,}))?)(?:([E])(([+-])([0123456789]+))|)))

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:
----------------------------------------------------------------------
    (?i)                     set flags for this block (case-
                             insensitive) (with ^ and $ matching
                             normally) (with . not matching \n)
                             (matching whitespace and # normally)
----------------------------------------------------------------------
    (                        group and capture to \2:
----------------------------------------------------------------------
      [+-]?                    any character of: '+', '-' (optional
                               (matching the most amount possible))
----------------------------------------------------------------------
    )                        end of \2
----------------------------------------------------------------------
    (                        group and capture to \3:
----------------------------------------------------------------------
      (?=                      look ahead to see if there is:
----------------------------------------------------------------------
        [.]?                     any character of: '.' (optional
                                 (matching the most amount possible))
----------------------------------------------------------------------
        [0123456789]             any character of: '0', '1', '2',
                                 '3', '4', '5', '6', '7', '8', '9'
----------------------------------------------------------------------
      )                        end of look-ahead
----------------------------------------------------------------------
      (                        group and capture to \4:
----------------------------------------------------------------------
        [0123456789]*            any character of: '0', '1', '2',
                                 '3', '4', '5', '6', '7', '8', '9' (0
                                 or more times (matching the most
                                 amount possible))
----------------------------------------------------------------------
      )                        end of \4
----------------------------------------------------------------------
      (?:                      group, but do not capture (optional
                               (matching the most amount possible)):
----------------------------------------------------------------------
        (                        group and capture to \5:
----------------------------------------------------------------------
          [.]                      any character of: '.'
----------------------------------------------------------------------
        )                        end of \5
----------------------------------------------------------------------
        (                        group and capture to \6:
----------------------------------------------------------------------
          [0123456789]             any character of: '0', '1', '2',
          {0,}                     '3', '4', '5', '6', '7', '8', '9'
                                   (at least 0 times (matching the
                                   most amount possible))
----------------------------------------------------------------------
        )                        end of \6
----------------------------------------------------------------------
      )?                       end of grouping
----------------------------------------------------------------------
    )                        end of \3
----------------------------------------------------------------------
    (?:                      group, but do not capture:
----------------------------------------------------------------------
      (                        group and capture to \7:
----------------------------------------------------------------------
        [E]                      any character of: 'E'
----------------------------------------------------------------------
      )                        end of \7
----------------------------------------------------------------------
      (                        group and capture to \8:
----------------------------------------------------------------------
        (                        group and capture to \9:
----------------------------------------------------------------------
          [+-]?                    any character of: '+', '-'
                                   (optional (matching the most
                                   amount possible))
----------------------------------------------------------------------
        )                        end of \9
----------------------------------------------------------------------
        (                        group and capture to \10:
----------------------------------------------------------------------
          [0123456789]             any character of: '0', '1', '2',
          +                        '3', '4', '5', '6', '7', '8', '9'
                                   (1 or more times (matching the
                                   most amount possible))
----------------------------------------------------------------------
        )                        end of \10
----------------------------------------------------------------------
      )                        end of \8
----------------------------------------------------------------------
     |                        OR
----------------------------------------------------------------------
    )                        end of grouping
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
[download]

Please also see perlre, perlretut, and perlrequick. There are also a number of on-line regex explainers, but I'm not familiar enough with them to recommend any particular one. (Update: Actually, davido has a nice regex tester which ends up giving a fair amount of explanation, or at least enlightenment. See his personal node for a link)

Update: Caution: YAPE::Regex::Explain only supports regex features added through Perl version 5.6.