In the form, avoid putting the email address in the name or value tags of the checkbox, as there is the possibility of someone using your script to send emails to unintended recipients. Use the ID from the database to identify the recipients.

<input type="checkbox" name="<?=$result['id']?>" value="1">

In the script that handles the form, call the list of email addresses again and use a while loop to progress through them. Check if the box was checked and then build a long comma-separated string to put in the mail command.

if($$result['id']==1) {

    $to.=$result[name].' <'.$result['email'].'>, ';

}

The trailing comma and space on that string might cause a problem, so trim it:

$to=substr($to, 0, -2);

Then call the mail command:

mail($to, 'subject', 'body');