I am guessing, but here goes:
1. What you are seeing is Ajax in action - partial page refreshes. Look up update panel in ASP.Net AJAX for details. Suggested links are below:
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I am sure you can find more on Google. You really need to understand Javascript to use this effectively.
2. Whether this site uses database or not is immaterial - the reality is that some sort of persistent storage is required if you want to.. ummm..persist information between requests.