Azure Virtual Desktop or AVD (also sometimes incorrectly referred to online as Microsoft Virtual Desktop or MVD, and also as its previous name of Windows Virtual Desktop, or WVD) is a set of technologies from Microsoft Azure that enables IT professionals and Managed Service Providers (MSPs) to create Windows 10 virtual desktops in Azure.  AVD was launched in 2019 and is the evolution of Microsoft’s Remote Desktop Services (RDS) technology. Azure Virtual Desktop consists of 4 primary innovations: 

Windows 10 multi-user operating system, which allows multiple concurrent users to use a single Azure virtual machine as a desktop.  Prior to AVD, this was only possible with the Windows Server operating system. 
User profiles are handled independently of the virtual machine that serves are the user’s desktop.  These profiles are placed in containers and the containers are stored separately from the desktop VM in Azure.  This is enabled by FSLogix technology that Microsoft purchased in 2018.
Microsoft Azure has a new Platform-as-a-Service (PaaS) offering that contains the management and connection broker functionality for AVD.  It is the service that determines which users end upon which Azure virtual machine when they connect.  Before Windows Virtual Desktop, this was handled by RDS server roles such as RD Gateway, RD WebAccess, RD Connection Broker, and RD License Server. 
Licensing for AVD has been drastically simplified from prior virtual desktop technologies like RDS.  AVD rights are included at no additional charge with multiple Windows 10 subscriptions including Microsoft 365 and Windows 10 Enterprise.

There are two cost components to AVD:  License and Azure infrastructure. 

Microsoft License – Azure Virtual Desktop is an entitlement of a Windows 10 subscription license.  This license can be purchased as part of Microsoft 365 Business/E3/E5/A3/A5 or as a standalone subscription (e.g. Windows 10 Enterprise E3).  If you already own one of these licenses there is no additional cost to use WVD from a software perspective.   

If you don’t already have a Windows 10 subscription license, then the least expensive option that covers AVD is Windows 10 Enterprise E3 for $7/user/month.  AVD license covers the cost of the operating system (Windows 10 single user and multi-session) and the use of the AVD management service that’s hosted by Microsoft in Azure.   

This license also replaces the need to pay for Windows Server OS license in Azure and the RDS license, since neither of these technologies is used to deliver Windows Virtual Desktop. It is important to note that AVD covers only Azure virtual machines and cannot be used to license on-premises deployments or other clouds.    

Azure Infrastructure – Once the license portion of AVD is covered, what remains is the cost of Azure infrastructure to run the virtual machines that users will connect to and use as their desktop.  In addition to the desktop VMs, you will need a place to store users’ profile containers and Active Directory (in addition to Azure AD).  Profile containers can be stored in Azure Files or on a Windows File Server VM in Azure, and Active Directory can be Azure AD DS or traditional AD running a Windows Server VM in Azure.   

The cost of all these components will include the virtual machines (compute), storage (disks and files), networking (egress bandwidth), etc.  The precise cost will depend on the number of users, amount of storage per user, how many and what types of applications the users use and many other factors.  The easiest way to calculate the precise cost is to use a tool like Microsoft Azure Cost Estimator to have it architect the infrastructure and figure out all the costs.  As a rough range, the Azure infrastructure cost component for pooled desktop users (those sharing a VM or set of VMs) would be in the $10-$30/user/month, and for a personal desktop user (those with dedicated desktop VMs) being in the $60-$130/user/month range.