Most common way to do this is to make the checkboxes submit as an array (e.g. add '[]' onto the end of their names, such as 'delete[]') and set their value equal to the rows' ID numbers (or whatever unique data you use to identify rows in your table).
Then, in your processing script, you'd simply verify that $_POST['delete'] is an array, and run a query such as:
$ids = array_map('mysql_real_escape_string',$_POST['delete'])
$query = 'DELETE FROM person WHERE id IN (' . implode(',',$ids) . ')';
Note that the above code assumes you used numeric numbers (e.g. an AUTO_INCREMENT column) to identify your rows.
EDIT: Also, you shouldn't use 'SELECT *' but instead only SELECT the column(s) you're actually going to need data from.