Why we design distributed availability group?
What is the distributed high availability benefit which we can not leverage with traditional AG? If you can explain one scenario of failover which we can not avail in traditional AG?


Distributed availability groups are a new feature introduced in SQL Server 2016, as a variation of the existing Always On Availability Groups feature. No announcements have been made as to whether future versions of SQL Server will allow previous versions to participate in the same distributed availability group. If that scenario were enabled, it would allow distributed availability groups to be part of a SQL Server version upgrade plan.

For your understanding I have just copy and paste the appropriate stanza articles from the documentation for Distributed availability groups:


  A distributed availability group is a special type of availability group that spans two separate availability groups. The underlying availability groups are configured on two different Windows Server Failover Clustering (WSFC) clusters. The availability groups that participate in a distributed availability group do not need to be in the same location. They can be physical, virtual, on-premises, in the public cloud, or anywhere that supports an availability-group deployment. As long as two availability groups can communicate, you can configure a distributed availability group with them.
  
  The following figure shows a high-level view of a distributed availability group that spans two availability groups (AG 1 and AG 2), each configured on its own WSFC cluster. The distributed availability group has a total of four replicas, with two in each availability group. Each availability group can support up to the maximum number of replicas, so a distributed availability group based on Standard Edition can have up to four replicas, and one based on Enterprise Edition can have up to 18 total replicas.
  
  
  
  The individual WSFC clusters and their corresponding availability groups follow traditional rules. That is, they can be joined to a domain or not joined to a domain (Windows Server 2016 or later). When two different availability groups are combined in a single distributed availability group, there are four scenarios:
  
  
  Both WSFC clusters are joined to the same domain.
  Each WSFC cluster is joined to a different domain.
  One WSFC cluster is joined to a domain, and one WSFC cluster is not joined to a domain.
  Neither WSFC cluster is joined to a domain.
  




Your second question:


  In which scenario the design of distributed AG is preferable?


Again, quoting from the same documentation:


  Here are the three main usage scenarios for a distributed availability group:
  
  
  Disaster recovery and easier multi-site configurations
  Migration to new hardware or configurations, which might include using new hardware or changing the underlying operating systems
  Increasing the number of readable replicas beyond eight in a single availability group by spanning multiple availability groups