A single page application means that there won't be any need for POSTBACK and page reloading for new data. Yes, Ajax will do it and will download the data for your pages.
There are many already developed plugins for these features, Knockout.js and Angular.js is a part of this. Since you're talking about ASP.NET, I will forward you to,
http://www.asp.net/single-page-application[
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You can learn how to create "Single Page Applications" from there, you can also conduct your
research there and get the results. Wordpress, Drupal are just CMS, they will manage your content of the website however it is better to create your own to get more control over your system. Once you've created the Single Page template, simply upload it to the hosting server don't fall for a CMS.