When the user selects options in your form and submits it, this will run a PHP script on the server. The server retrieves the option parameters, and uses them to construct a SQL query. For instance, the script might contain something like:
$criteria = array();
if (isset($_POST['calories'])) {
$criteria[] = 'calories < '.$_POST['calories']);
}
if (isset($_POST['time'])) {
$criteria[] = 'cooking_time < '.$_POST['time']);
}
...
$query = 'SELECT * FROM recipes WHERE '.implode(' AND ', $criteria);
You use a library like mysqli or PDO to perform the query and get the results. Then you loop through the results, and format them into an HTML table which will be returned to the user as the resulting web page.
Or the PHP script could return the results as JSON data. Your web page could use AJAX to get this data from the server, then use JavaScript to format it into a table.