I'd probably rewrite this way:

use strict;
use warnings;

my $records_wanted = 10;

my $minlength=3;
my $maxlength=6; # max length of the record - will be specified by use
+r

my @alphabet = ( 'a' .. 'z', 'A' .. 'Z', '0' .. '9' );

my $records_made = 0;
while ( $records_made++ < $records_wanted ) {
    my $record = '';
    my $record_length
        = $minlength + int rand( $maxlength - $minlength + 1 );

    warn "rlength: $record_length\n";

    while ( length $record < $record_length ) {
        $record .= $alphabet[ rand @alphabet ];
    }
    warn "record: $record\n";
}
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A few notes...

• Randomly selecting an element from some array is pretty easy ($foo[ rand @foo ]), and $#foo is not the same as scalar @foo.
• If you name your variables better (e.g., $records_wanted, $records_made), you need fewer comments.
• This modifies $minlength: "$rlength=$minlength+=int(rand($maxlength))".
• If you use warn for your debugging output, it's easier to find later when it's time to remove them.

Sample output:

rlength: 4
record: 3J9J
rlength: 5
record: 9NxuW
rlength: 5
record: rwtwj
rlength: 3
record: AVY
rlength: 3
record: WPY
rlength: 5
record: wxeTn
rlength: 5
record: 86JH1
rlength: 6
record: PwLx2X
rlength: 4
record: nXuG
rlength: 4
record: cpXk
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