It's documented in perlvar: $*. The docs also say what you should use instead:

You should use the /s and /m regexp modifiers instead.

$* was used to enable multi-line matching in regular expressions. It's been replaced by the m and s flags. m lets ^ and $ match at line ends. s lets . match new line characters.

In isolation $* doesn't mean anything. You need to look for uses of regular expression matches to figure out what it might be doing. Look for uses of =~ and examine the code around it.

It was the same as using /m on all your match and substitution operators, except it overrode instructions to turn /m off.

For example, qr/foo$/ shouldn't match "foo\nbar\n" even if it's used as /$re/m.

$ perl5010 -le'
   $re = qr/foo$/;
   print $re;
   print "foo\nbar\n" =~ /$re/m ?1:0
'
(?-xism:foo$)   # -m: Turn /m off.
0
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But it did before 5.10

$ perl5008009 -le'
   $re = qr/foo$/;
   print $re;
   print "foo\nbar\n" =~ /$re/m ?1:0
'
(?-xism:foo$)
1               # Matched as if /m was on for the subpattern.
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This was fixed, but there was no way of fixing $* which had the same error.

$ perl5008009 -le'
   $re = qr/foo$/;
   print $re;
   local $* = 1;
   print "foo\nbar\n" =~ /$re/ ?1:0
'
(?-xism:foo$)
1
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So it was dropped.

Not even deprecated anymore. I believe current Perl has removed it. As of 5.20 (possibly earlier) if you use it:

perl -E '$*=1;'
$* is no longer supported at -e line 1.
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If you want the full explanation of what it used to do, look at an older version of the documentation. 5.8.9 ought to do, and it's available on perldoc.perl.org: http://perldoc.perl.org/5.8.9/perlvar.html:

Set to a non-zero integer value to do multi-line matching within a string, 0 (or undefined) to tell Perl that it can assume that strings contain a single line, for the purpose of optimizing pattern matches. Pattern matches on strings containing multiple newlines can produce confusing results when $* is 0 or undefined. Default is undefined. (Mnemonic: * matches multiple things.) This variable influences the interpretation of only ^ and $ . A literal newline can be searched for even when $* == 0 .

Apparently already unsupported in Perl 5.14:

$ perl -E '$*=1;'
$* is no longer supported at -e line 1.

$ perl -v

This is perl 5, version 14, subversion 4 (v5.14.4) built for cygwin-th
+read-multi
(with 7 registered patches, see perl -V for more detail)

Copyright 1987-2013, Larry Wall

Perl may be copied only under the terms of either the Artistic License
+ or the
GNU General Public License, which may be found in the Perl 5 source ki
+t.

Complete documentation for Perl, including FAQ lists, should be found 
+on
this system using "man perl" or "perldoc perl".  If you have access to
+ the
Internet, point your browser at http://www.perl.org/, the Perl Home Pa
+ge.
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