To create these folders you need to have Windows Phone 8.1 Update installed on your phone
If you have paid attention to Microsoft’s app management on any of the Windows Phone then you must have realized that their approach for this purpose has always remained very simplistic and to the point. What we have noticed so far is that they usually tend to avoid the folder interfaces that iOS and Android have adopted with the company’s "Metro-style" interface. However, this trend is about to take a turn for better. There was recently a support article on the Microsoft’s Windows Phone site and though it has been removed now, it was there long enough for us to catch a glimpse.
This particular article revealed what the company has been planning regarding the support for folders for apps on the Start Screen. This is going to work just like things go about for the iOS where you drag one Tile on top of another and it creates a folder that can then be renamed. In this way users can access the apps while they are inside the folder.
However, in order for these folders to work on your devices, you should make sure that you have Windows Phone 8.1 Update installed on your phone. So this makes it clear that the functionality of this feature is coming to an update rather than the actual OS itself. According to The Verge, the Windows Phone 8.1’s first update has gone into the final testing stage and is ready to debut in July or August.