As BrowserUK says, it's the line number of the most recently opened filehandle.

Here's a (slightly contrived) example:

#!/usr/bin/perl

use strict;
use warnings;

use FileHandle;

my $iam = $0;
my $fh = new FileHandle;
open($fh, "<", $iam) or die "Can't open myself:  '$iam' ($!)\n";

my $cnt = 15;
while (my $line = <$fh>) {
    chomp $line;
    printf "%2d:  %s\n", (10 / $cnt--), $line;
}
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When saved as the file "mytest", and run, it errors out on the 15th line, where a division by zero error occurs:

Illegal division by zero at mytest line 15, <GEN0> line 16.
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