What you are looking at here is a server push
implementation. That means when some notification/action happens in the server, it should push a notification to your rails app. The difference with @manju's answer is, its proposing a a solution based on your clients browser will call the server periodically for new notifications.
There are two main ways to do this.
1 - Using some third party SASS solutions. (easy way, but cost money ;))
Fire base , allows you to send push notifications to clients.
pusher is another provider offers the same kind of functionalists.
Read their documentations, normally each of them have gems you can easily integrate to your rails app.
2 - Implement your own push server
You can implement your own push server with rails, and integrate to your app.
Faye is a one option,
But more exiting thing is Rails5 will have Action Cable which tries to solve the same issue. action cable gem
and there are articles showing action cable with rails4 apps (you dont have to wait till rails5 comes out) , but I haven't used it personally yet.
HTH