The sites you are asking about are normal WordPress sites that are displaying several posts on the front page.

If you go into the dashboard Settings->Reading->Blog pages show at most and select 4 you will get the most recent 4 posts displayed. By manipulating the date you will get the effect that you want.

Hi,

I don't think you looked at the website and understood my question... My website also runs Wordpress and I understand what you mean about Recent Posts.

However, in the images I uploaded I highlighted the "Featured Posts" in square boxes above the websites posts. I am wondering how they did it and if there is any plugin that can do the same?

Thanks!

you can easily integrate it into your wordpress website if you are use wordpress framework .some plugins available on net

I use a plugin called Related Posts by Zemanta, you can position them anywhere you want. It supports relationships to your own posts, or third party content from other websites.

Here's an example on one of my sites with the related posts at the bottom: http://www.rareartifact.com/tools/du...procating-saw/

Any part of any WP theme template can be "widgetized" i.e. to create a section that can display widgets.
1. Create a widget area
2. Pick you 'featured...' plugin; install and activate it
3. Add it to your area