There are 2 different meanings to this:

First is to really persist the data even when the application restarts

• This is well explained in the above post from @hubertlepicki

Second is to keep data only in running application [keep a state] (like an object instance in OO languages)

• Manual state struct which you’ll pass around in the module
  • I use this option if I need to keep just a simple state in one module
• You can use Agents: http://elixir-lang.github.io/getting-started/mix-otp/agent.html
  • I use this if I need to keep state between more modules
• You can create a GenServer: https://hexdocs.pm/elixir/GenServer.html
  • a bit more robust solution.

The above state won’t survive the application crashes/restarts though, so you usually use the mix of GenServer/Agent and Database/Amnesia/DETS, etc.

This is a great article that talks about the different states , it is for Erlang, but it explains theory well.
http://learnyousomeerlang.com/building-applications-with-otp#the-onion-layer-theory

Cheers mate