...
my $listbox = $files_frame->Scrolled("Listbox",
    -scrollbars => "oe",
    -selectmode => "extended")->pack;
$listbox->insert('end', @files);

$exit_frame->Button(-text => "Files",
    -command => [ \&print_filenames, $listbox ])->pack;
$exit_frame->Button(-text => "Exit",
    -command => sub { exit; })->pack;

...


sub print_filenames
{
# callback for the "File" Button
    my $listbox = shift;
    my @selected_files = $listbox->curselection;
    for (@selected_files) {
        my $file = $listbox->get($_);
        print "$file\n";
    }
}