As sujay said,XAMPP/WAMP/any other web server is necessary on computer which is being used to demo the site because a site is always hosted on a web server.No, I want to store it on my own laptop and then take it somewhere where there is no connectivity and then open a browser and show the other person how it works.
As far as the files (pages) are stored in .html format, they will behave like the real webpages in offline mode to I will also suggest you to try out FTP as the website is tested on it before launching it online.