Why use admin-ajax.php when loading pages through AJAX?

I have used this tutorial to implement ajax page transitions on my website. After looking in to some issues, I found that on most forum post people suggest to "use" admin-ajax.php.

I looked into that but I'm afraid I don't really understand how it works.

Here's my current page-transition.js, which is starting to work pretty good. What would change (not necesseraly in the code, but more in the way it works) if I were to use admin-ajax.php, and is it really "mandatory" ?

jQuery(document).ready(function (event) {

    // get rooturl via localize script
    var rootUrl = aws_data.rootUrl; 
    var isAnimating = false, 
        newLocation = '', 
        firstLoad = false;

    // Internal Helper
    $.expr[':'].internal = function(obj, index, meta, stack){
        // Prepare
        var
            $this = $(obj),
            urlinternal = $this.attr('href')||'',
            isInternalLink;

        // Check link
        isInternalLink = urlinternal.substring(0,rootUrl.length) === rootUrl || urlinternal.indexOf(':') === -1;

        // Ignore or Keep
        return isInternalLink;
    };



    //trigger smooth transition from the actual page to the new one on relevant links
    $('main').on('click', 'a[href]:internal:not(.no-ajaxy,.love-button,[href^="#"],[href="#"],[href*="#respond"],[href*="wp-login"],[href*="wp-admin"])', function (event) { 
        event.preventDefault();
        //detect which page has been selected
        var newPage = $(this).attr('href');
        //if the page is not already being animated - trigger animation
        if (!isAnimating) changePage(newPage, true);
        firstLoad = true;
    });
    //detect the 'popstate' event - e.g. user clicking the back button
    $(window).on('popstate', function (e) {
        if (firstLoad) {
            /*
            Safari emits a popstate event on page load - check if firstLoad is true before animating
            if it's false - the page has just been loaded 
            */
            var newPageArray = location.pathname.split('/'), //this is the url of the page to be loaded 
                //newPage = newPageArray[newPageArray.length - 1];
                newPage = window.location.href;
            if (!isAnimating && newLocation != newPage) changePage(newPage, false);
        }
        firstLoad = true;
    });

    function changePage(url, bool) {
        isAnimating = true;
        // trigger page animation
        $('body').addClass('page-is-changing');
        $('.cd-loading-bar').one('webkitTransitionEnd otransitionend oTransitionEnd msTransitionEnd transitionend', function () {
            loadNewContent(url, bool);
            newLocation = url;
            $('.cd-loading-bar').off('webkitTransitionEnd otransitionend oTransitionEnd msTransitionEnd transitionend');
        });
        //if browser doesn't support CSS transitions
        if (!transitionsSupported()) {
            loadNewContent(url, bool);
            newLocation = url;
        }
    }

    function loadNewContent(url, bool) {

        url = ('' === url) ? rootUrl : url; 
        //var newSection = 'cd-' + url.replace(rootUrl, ""); 
        var section = $('<div class="cd-main-content"></div>');

        $.ajax({url: url, 
            success: function(data){
                data = data.replace("<body", "<container").replace("body>", "container>");
                var classes = $(data).filter("container").attr("class"); 
                $("body").attr("class", classes + " page-is-changing"); 
            } 
        });

        section.load(url + ' .cd-main-content > *', function (response, status, xhr) {


            // load new content and replace <main> content with the new one
            $('main').html(section);
            //if browser doesn't support CSS transitions - dont wait for the end of transitions
            var delay = 1200; 

            //function to execute after dom is loaded
            $(document).foundation();
            makeFooterSticky();
            window.scrollTo(0, 0);
            $(".ajax-load-more-wrap").ajaxloadmore();
            //ga('send', 'pageview', window.location.pathname);

            setTimeout(function () {
                //wait for the end of the transition on the loading bar before revealing the new content
                $('body').removeClass('page-is-changing');
                $('.cd-loading-bar').one('webkitTransitionEnd otransitionend oTransitionEnd msTransitionEnd transitionend', function () {
                    isAnimating = false;
                    $('.cd-loading-bar').off('webkitTransitionEnd otransitionend oTransitionEnd msTransitionEnd transitionend');
                });
                if (!transitionsSupported()) isAnimating = false;
            }, delay);
            if (url != window.location && bool) {
                //add the new page to the window.history
                //if the new page was triggered by a 'popstate' event, don't add it
                window.history.pushState({
                    path: url
                }, '', url);
            }
        });

    }

    function transitionsSupported() {
        return $('html').hasClass('csstransitions');
    }
});