Asynchronous Postback means it is a postback event occurs to a particular part of the page, for which the user has given asynchronous client side postback event. Mainly this can be done by using ASP.NET Ajax control called Update panel
In Asynchronous way from client sends only relevent information to the server and server process the request and give the reply. From this reply client extract the required information and apply the client logic(for example update the UI).Internally browser use XMLHTTP for asynchronous communiction.It sends the request and register a call back function which is getting called once the reply received from the server.NOTE:XMLHTTP can be used to in Synchronous fashion also.
refer http://www.adaptivepath.com/publications/essays/archives/000385.php to know more about internal working of AJAX.
Asynchronous Postback means it will only part of page will be postback frequently without affecting the whole page.
How Can we do this-Simpal,By using Asp.net Ajax Control