Linen has what's called a featured slider option, where you can highlight certain posts, as you see in the demo. You can set that up under Appearance > Theme Options, by clicking the "Featured slider" tab:
https://verticalviv.wordpress.com/wp-admin/themes.php?page=ttf-admin.php
You can learn more about how to set up Linen here:
http://theme.wordpress.com/themes/linen/
All premium themes also have their very own support forums, where you can get help directly from the developers. Here's the one for Linen:
http://premium-themes.forums.wordpress.com/forum/linen
Just let us know if you get stuck!