shell> perl -MYAPE::Regex::Explain -e \
'print YAPE::Regex::Explain->new(q{^[\w.-]+\@(?:[\w-]+\.)+\w+$})->explain()'
The regular expression:

(?-imsx:^[\w.-]+\@(?:[\w-]+\.)+\w+$)

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):
----------------------------------------------------------------------
  ^                        the beginning of the string
----------------------------------------------------------------------
  [\w.-]+                  any character of: word characters (a-z, A-
                           Z, 0-9, _), '.', '-' (1 or more times
                           (matching the most amount possible))
----------------------------------------------------------------------
  \@                       '@'
----------------------------------------------------------------------
  (?:                      group, but do not capture (1 or more times
                           (matching the most amount possible)):
----------------------------------------------------------------------
    [\w-]+                   any character of: word characters (a-z,
                             A-Z, 0-9, _), '-' (1 or more times
                             (matching the most amount possible))
----------------------------------------------------------------------
    \.                       '.'
----------------------------------------------------------------------
  )+                       end of grouping
----------------------------------------------------------------------
  \w+                      word characters (a-z, A-Z, 0-9, _) (1 or
                           more times (matching the most amount
                           possible))
----------------------------------------------------------------------
  $                        before an optional \n, and the end of the
                           string
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------