Ajax is the process of getting data from the server to the browser or page without reloading the whole page. jQuery provides functions to manage Ajax transactions (as do all JS libraries).
$("body").html(data) means this:
$ is the jQuery object (shortcut).
"body" is a HTML selector (same as you might use in CSS). In this case it will get all <body> tags, of which there should be exactly 1.
data will be the response from your server side script (the data of the ajax transaction) and the .html() function call will set the innerHTML of <body> to that data.
That line of code will be called when the the Ajax transaction finishes, and it will set the content of <body> to be whatever your .php script displays.