I developing the web site using PHP. Can anybody please tell me, how to update part of web page without reloading the whole page. If possible, please provide sample code.
Welcome to the SP forums.
Like you wrote in the title of this post, with AJAX.
If you google for it, or do a search in this forum, you'll find tons of examples and tutorials. Please try some of them, and if there's something specific you don't understand, feel free to ask.
jQuery takes a lot of the pain out of AJAX so I would suggest you head over there and have a look at what it can provide.