What do you expect $j to be when the callback function gets called?  You have to somehow pass it as an argument to the routine.  There are two ways to pass the value:

Either specify an array(ref) to the -command option

...
for my $i (0...$#a)
{
    $f->Checkbutton(-text => $a[$i], -command => [ \&fun, $i ] )->pack
+();
}
MainLoop;

sub fun
{
    my $j = shift;
    print $a[$j];
}
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Or use a closure

...
for my $i (0...$#a)
{
    $f->Checkbutton(-text => $a[$i], -command => sub { fun($i) } )->pa
+ck();
}
...
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There is a third option, don't pass it any arguments

use Tk;
$mw = tkinit;
for(1..4){
    $mw->Checkbutton(
        -text => qq/check it $_/,
        -command => \&f,
    ) ->pack;
}
MainLoop;
sub f {
    my $b = $Tk::event->W;
    warn join q/ /, $b->{Value}, $b->cget(q/-text/);
}
__END__
1 check it 3 at - line 14.
0 check it 3 at - line 14.
1 check it 3 at - line 14.
0 check it 3 at - line 14.
1 check it 3 at - line 14.
0 check it 3 at - line 14.
1 check it 3 at - line 14.
0 check it 3 at - line 14.
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First off, if you added

use warnings;
use strict;
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foreach $i (1...20)   # that ... should be ..
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If you are a student, I wouldn't even accept this as a valid submission. Here is some unflawed code for you to look at.

#!/usr/bin/perl
use warnings;
use strict;
use Tk;
use Tk::Pane;

my @a=qw/one two three four five six seven eight nine ten/;

my $mw = MainWindow->new;

$mw->geometry('200x200');

my $f = $mw->Scrolled("Frame",-borderwidth => 3, -relief => 'groove',-
+height=>20)
        ->pack(-expand=> 1, -fill=>'both');


foreach my $i (0 .. 19){  # this should be foreach my $i (@a), but it'
+s your code :-)
print "$i\n";

my $c = $f->Checkbutton(-text=>$a[$i],-command=>[ \&fun, $a[$i] ] )->p
+ack();
   $i++;
  }

MainLoop;

sub fun{
  print "@_\n";
} 

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