I am by no means an expert in Microsoft Licensing and you should ALWAYS consult with your preferred vendor to arrive at a warm fuzzy feeling when it comes to license compliance (is there such a thing with regards to licensing?). If you haven't guessed already this article is going to be Microsoft center, albeit you can have linux and other OS based virtual desktops.
To start off, VDI is the acronym for Virtual Desktop Infrastructure. In short this is the running of (usually multiple) virtual desktop operating systems on a physical system and accessing them remotely. There are troves of articles out on the net about the merits, challenges, and use cases for VDI.
The initial thought for licensing these virtual instances of a desktop OS is often simply to go buy a license for each one and be done. That is not the case when it comes to Microsoft Windows. Microsoft realized there is value in running their software this way and subsequently created new licensing for such use cases. This is where VDA comes into play.
Two methods exists, that I'm aware of, for properly licensing virtual instances of Windows desktops: VDA and SA. SA or Software Assurance comes into play for corporate systems that have their Desktop OS SA maintained. These systems can be used to access VDI instances. The other is the VDA license. The VDA license is a bit more flexible (and costly) than SA because it can apply to a non Microsoft client device as well as non-corporate devices (contractor, employee owned PC,etc). You can read lots more about Microsoft and Virtual Desktops on Microsoft's Website.
The big question that I've always had until recently around the VDA license is: is it just an "Access Right" license or does it also include the virtual desktop OS? In the Microsoft world "Access" licenses, or CALs as they are often called, are very common - so quite naturally I wondered if the annual subscription based VDA license was only a "CAL" or more so. So after receiving a not so clear response from my Microsoft vendor, I consulted Google for other's experiences. I ran across this VMware Community thread some time ago and subscribed to it with hopes a more definitive update would be posted. Just today a post came through from MoffattThomas, quoting a Microsoft representative stating(summarized): the VDA includes the OS key for the virtual desktop. So there you go - Virtual OS and access rights!