I m building a facebook application. In the application setting, there is a option to enable the Oath authentication. So, what is the advantage of using Oath Authentication over normal authentication....
I assume you are referring to the beta OAuth setting in the Canvas settings tab.
OAuth authentication in this respect means that Facebook sends you a signed_request facebook parameter in the query string instead of the normal canvas session information, see here more more details of signed_request.
You do not need to turn this on if you do not want to. Assuming you are using the PHP SDK you can use any authentication method you want (cookies from JavaScript, signed_requests or session variables).
The advantage to OAuth is the added level of security and the fact it is an open standard. Since you are just building your application you will not be using any of Facebook's old proprietary authentication methods and so you will be using OAuth no matter which of the above methods you use.
As far as you are concerned you can leave the setting off for now until it comes out of beta. When it does switching it on will mean no changes to your code as the PHP SDK handles it out of the box!