Enhanced business intelligence. Using SharePoint as a platform to expose business intelligence and big data reports had its coming-out party with the 2010, but the capabilities have expanded in the 2013 release to really make SharePoint the choice to dig deeper into business insights and analytics. Integration between SharePoint and Excel is even tighter, too.
Finally, the PowerPivot program has gotten even more powerful in SharePoint 2013; you can work with billions and rows and columns directly in memory, while features such as PerformancePoint Services, Dashboard Designer and Visio Services all work together to paint a picture of your business' health and metrics.
End-user training. SharePoint 2013 includes a new feature called "deferred site collection upgrade." This essentially lets a specific set of site collections run under SharePoint 2010 while SharePoint 2013 code is installed. You are basically running SharePoint 2010 code within the 2013 product, which makes it easier to test and maintain compatibility with any custom code and applications you have built on top of SharePoint.
It also eases the transition for your users between the look and feel of how SharePoint 2010 libraries and sites operates. You can get the benefit of deploying the new product while you manage the timeline on which you convert the look and feel of your site and turn on the new features and capabilities that face your end users. This is a good thing.
More, better, mobile device support. Of course tablets and smartphones are all the rage these days. With SharePoint sites becoming the home for more and more work product in all sorts of businesses, Microsoft had to address the problem of the poor SharePoint experience for mobile devices in previous versions.
There is now an HTML5 coded view known as the "contemporary" view that is optimized for speedy access across iPhones, iPads, Android, BlackBerry and Windows Phone devices. There is also new support for push notifications, so SharePoint 2013 can reach out and push a message to your device based on a variety of factors. Location awareness has been built in as well, if you plan to develop location-aware applications on top of the SharePoint platform.
SharePoint 2013 Concerns: The Onsite vs. Cloud Conundrum
Of course, SharePoint 2013 isn't all wine and roses. Here are two pain points: