Phoenix shares many features with Ruby on Rails, e.g. a strong MVC model, an integrated ORM, a routing system, etc. What Phoenix on Elixir excels at is concurrency and distributed computing. For applications, this means you can have many active web sockets, for instance, where Rails applications tend to break down when you have too many active connections. Phoenix uses erlang processes for these tasks, which are lightweight and can number millions on a single machine.
As an example, Heroku uses cowboy (the erlang web server that Phoenix uses) for load-balancing incoming connections to all Heroku applications. The erlang VM (BEAM) is great for these types of highly concurrent, highly available, distributed tasks. The original use case for erlang was highly available phone switching for Ericsson.