AJAX is a flexible and versatile tool that provides developers the possibility of creating improved applications, and an example of its functionality would be to check credentials upon sending them to the server. Given the asynchronous way in which AJAX works, the entire page doesn't have to be reloaded to receive new data, which is probably why WordPress is so compatible with AJAX and how it interacts with it.
AJAX, in its essence, is a combination of several programming languages, which would be XML and JavaScript. The name Asynchronous JavaScript and XML might or might not be self-explanatory, yet its function is to send data to the server by the means of JavaScript and then return this data in a different, now an XML format.
AJAX, in its manifestation, works to commit small changes or updates for the site visited by the user, without having to send a request for a full page load, meaning that it will be a more efficient way of committing locally rather than a global refresh...