Firebase is a NoSQL type database that makes use of sockets, which allows the client to receive information live - without having to make GET requests to the server.
This requires that when you set things up you 'subscribe' the client to the database/collection.
In terms of how you could use it in an application, that depends on the technologies you wish to use in your stack. The firebase website has documentation advising you on how to do this.
Also, if you are asking solely on the basis of wishing to have the functionality you have described; the Meteor framework comes with a sockets based, NoSQL, backend database which is very easy to implement; there is a tutorial here; https://www.meteor.com/tutorials/blaze/creating-an-app
