SharePoint 2013 is packed with a lot of bells and whistles as compared to its predecessor SharePoint 2010. But the features that really stands out are:
1) Device Channels - Design a Layout, Look and Feel specific to iPhone, Windows Phone, Surface and iPad
2) Cross Browser Compatibility (incl. mobile browser) - Full support for HTML5, CSS3, JQuery and all the good stuff
3) "One Search" Solution (no confusing FAST vs Enterprise Search) - Our Favorite feature especially the new “Continuous Crawl” option that will allow users to search all the time and trust the results. Also the new "Content Search Web Part" ROCKS!
4) Social Media and Gamification - Use Community Sites and Portal to promote discussion between site members and assign badges/points to members who answer questions
5) Design "Responsive" Websites - Friendly URLs, Design Manager (clear seperation of code from design), Device Channels (ability to target same content rendered differently on different mobile devices), Managed Navigation, Content Search Web Part etc all adds to the a simple yet enhanced web design and development user experience
6) SharePoint Apps and App Store - Build cool apps and add-ons for SharePoint and allow users to install "1-click install" apps similar to Google Play or Apple iTunes Store.