When you follow a podcast or station it will appear on your home screen and Library, giving you quick access when you want to listen.
For podcasts, your feed of latest episodes will be updated when a new episode is released from a podcast you follow. You will also receive a notification, which can be turned on or off in settings.
To learn how to follow a podcast or station see: How do I follow a podcast or station?
To turn on/off your notifications see: How do I manage notifications?