why not just use:
/\t\w+/

For cases where you're using it in a substitution operator (s///). The tab won't get included in the substitution.

what is $& ?

See perldoc perlvar for explanations of all of Perl's special variables. $& is the part of your string which matched the regex.

Some common usages of (?<=...), (?=...) and (?!...):

s/(?<=a)b/c/;       # Changes the 'a', but keeps the 'b'.

s/b(?=a)/c/;        # Changes the 'a', but keeps the 'b'.
/^(?=.*a)(?=.*b)/;  # Is equivalent to /a/ && /b/.

/a(?:(?!bcd).)*e/;  # (?:(?!...).)* is to regexp what
                    # [^...] is to characters.
                    # This example reads as:
                    # "Match 'a' followed by somethng which
                    # doesn't contain 'bcd', followed by 'e'."
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$& refers to "everything that was matched". It's what gets substituted in a substitution. Avoid actually using $&. It has side effects which can slow down other regexps in your program. It can easily be emulated using captures.

As others have mentioned, /(?<=\t)\w+/ does not include the tab in $& which contains the text that the regular expression matched. Perhaps some code might make it a little clearer:

#!/usr/bin/perl
use strict;

my $string = "Testing \tthis regex";

print $string, "\n";

$string =~ /(?<=\t)\w+/;
my $string1 = $&;

$string =~ /\t\w+/;
my $string2 = $&;

print "/(?<=\\t)\w+/:\n" . $string1 . "\n";
print "/\\t\w+/:\n" . $string2 . "\n";
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This is mostly useful for substitutions but hopefully my code makes it a little clearer as to what is going on. The output is as follows:

Testing         this regex
/(?<=\t)w+/:
this
/\tw+/:
        this
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