WAR files in Java can be seen as a "container" for Java applications, although that only works for Java, if you want to use the same process for Java and PHP applications, you need something that's standard between the two technologies, Docker gives you this - it allows you to package your application into a common format.
If you're just using .NET and Azure is taking care of everything, then not much benefits of using Docker. If you're mixing different versions of .NET and other technologies, then you might benefit from Docker. Also, if you want to run your workload on something like Kubernetes or Beanstalk, you'll be forced to package your applications in Docker containers.