So you're basically wanting to dump all of the entries to screen, allow the user to select certain rows, and then take the user's selection and output only those rows?
If you named the checkboxes like this:
<input type="checkbox" name="row[]" value="1">
(where 1 would be replaced with the 'ID' column for each row), then $_POST['row'] will be an array of ID values that the user selected (or it won't exist, if they didnt' select any).
You could then use that array of ID values to select the appropriate rows in the DB. Sample SQL query to do that:
$sql = 'SELECT col1, col2 FROM myTable WHERE id IN (' . implode(',', $_POST['row']) . ')';
Don't forget about data sanitization, however, to avoid SQL injection attacks. Something like this would be an easy way to ensure that you're only getting numerical values back:
$_POST['row'] = array_map('intval', $_POST['row']);
