Traditionally webpages required reloading to update their content. For web-based email this meant that users had to manually reload their inbox to check and see if they had new mail. This had huge drawbacks: it was slow and it required user input. When the user reloaded their inbox, the server had to reconstruct the entire web page and resend all of the HTML, CSS, JavaScript, as well as the user's email. This was hugely inefficient. Ideally, the server should only have to send the user's new messages, not the entire page. By 2003, all the major browsers solved this issue by adopting the XMLHttpRequest (XHR) object, allowing browsers to communicate with the server without requiring a page reload.
The XMLHttpRequest object is part of a technology called Ajax (Asynchronous JavaScript and XML). Using Ajax, data could then be passed between the browser and the server, using the XMLHttpRequest API, without having to reload the web page. With the widespread adoption of the XMLHttpRequest object it quickly became possible to build web applications like Google Maps, and Gmail that used XMLHttpRequest to get new map tiles, or new email without having to reload the entire page.
Ajax requests are triggered by JavaScript code; your code sends a request to a URL, and when it receives a response, a callback function can be triggered to handle the response. Because the request is asynchronous, the rest of your code continues to execute while the request is being processed, so it's imperative that a callback be used to handle the response.
Unfortunately, different browsers implement the Ajax API differently. Typically this meant that developers would have to account for all the different browsers to ensure that Ajax would work universally. Fortunately, jQuery provides Ajax support that abstracts away painful browser differences. It offers both a full-featured $.ajax() method, and simple convenience methods such as $.get(), $.getScript(), $.getJSON(), $.post(), and $().load().
Most jQuery applications don't in fact use XML, despite the name "Ajax"; instead, they transport data as plain HTML or JSON (JavaScript Object Notation).
In general, Ajax does not work across domains. For instance, a webpage loaded from example1.com is unable to make an Ajax request to example2.com as it would violate the same origin policy. As a work around, JSONP (JSON with Padding) uses <script> tags to load files containing arbitrary JavaScript content and JSON, from another domain. More recently browsers have implemented a technology called Cross-Origin Resource Sharing (CORS), that allows Ajax requests to different domains.