Your checkboxes can be named according to the rowID of the database, eg checkbox99 (where 99 is the rowID)
Then run
for($x=0;$x<$maxrowid;$x++)
{
if ($_POST['checkbox'.$x])==1)
{
$query=mysql_query("DELETE FROM `table` WHERE rowID='".$x."'");'
}
}
Something along those lines might work...
Or you could delete each row when the delet button is clicked.
Get Javascript to reload the page, with ?delete=yes&id=xx at the end
(xx is the row number to delete)
Then just do the delete SQL as above...