Ajax means Async JS and XML It will take the user input from user end and process and send back with page load .
"Ajax is the skin, php is the skeleton." Well basically, Ajax is the middle-man that interacts with the browser and the server such as php. The result is dynamic pages without the need to load a completely new page for inputs and outputs.
Here is 3-step tutorial I found on AJAX and PHP: Ajax/PHP Tutorial. It focuses on the basics of AJAX and then includes a small amount of PHP, so it's pretty simple and not anything outrageously difficult.
Use javascript as normal but within a PHP page. If you want to grab information from the PHP script again, you will have to reload the page (or an element of the page) as PHP is server side and Javascript is client side. Have worked with PHP and Javascript to AJAX successfully in the past. There's lots of examples out there on web
AJAX is used for front end development while PHP is the backend. So bascially AJAX is used the display something on your screen.