You need a RSS reader (also called feed reader or news aggregator).
As explained in How it works this reader (operating in the background) checks on a regular basis the feeds you are subscribed to and asks for your attention when it noticed new or changed content.
Where do I get this reader?
You can choose between online feed reader services or software running on your computer.
In many cases these readers are for free.
Popular RSS readers:
Online feed reader services
Personal computer software