What are AJAX and JQuery?

AJAX (Asynchronous Javascript and XML) is a group of related technologies used on the client-side to create asynchronous web applications.
HTML and CSS can be used in combination to mark up and style information. The DOM is accessed with JavaScript to dynamically display, and to allow the user to interact with the information presented. JavaScript and the XMLHttpRequest object provide a method for exchanging data asynchronously between browser and server to avoid full page reloads.

XMLHttpRequest

XMLHttpRequest has an important role in the Ajax web development technique. It is an API available in web browser scripting languages such as JavaScript. It is used to send HTTP or HTTPS requests directly to a web server and load the server response data directly back into the script withou need to page refresh or reload.
The data might be received from the server as XML text or as plain text. Data from the response can be used directly to alter the DOM of the currently active document in the browser window without loading a new web page document.

Using AJAX

To use AJAX, you must send XMLHttpRequest to server and get returned response; then handle the response and DOM by Javascript to do changes needed.
Javascript libraries or frameworks like JQuery do the same thing but with a more simple syntax. These libraries are debugged perfectly and checked compatibility of the commands with different browsers.
ASP.Net (.Net framework 3.5+) as a server side web programming language uses internal AJAX Javascript library and AJAX controls like ScriptManager and UpdatePanel for partial page rendering and updating; these components make the use of AJAX technology very simple.

JQuery

JQuery is not a new technology or script language. It is a library (framework) wrote in Javascript. It has a more simple syntax for many of Javascript commands; it also has many useful functions like fadeIn and fadeOut that make the programming very simple and more creative. This library provides functions for use of AJAX technology too. One of the most important features of JQuery is its small size.