Then do this. Make your checkboxes an array by specifing [] after the name (they all have the same name)
Ex: <input type="checkbox" name="var[]" value="1">
<input type="checkbox" name="var[]" value="2">
The only difference from this and your code is that the value should be the id for each product, so it should be dynamic. Select the id from your database, then do
<form method="post" action="processing_page.php">
while ($row = mysql_fetch_array($query)) {
echo $row["product_name"] . " <input type='checkbox' name='var[]' value='" . $row["id"] . "'><br>";
}
echo "</form>\n";
Now when they submit, you'll have the array $var with the values (which would be the id's) of the products. Then, just use a select query to select all those values from the database.
$query = "SELECT * FROM your_table WHERE id IN ('" . implode("','", $_POST['var']) . "')";
$result = mysql_query($query);
That will select everything from the table, your_table WHERE the id equals any of the values they selected using the checkboxes. Then, just take that and display the results.
Cgraz