By favouriting a new podcast or station, you will see it automatically appearing in your feed as soon as a new episode is released. You will also receive a notification letting you know that the show is ready for you to stream. Favouriting a station will add the station to your stations on the radio page.
To learn how to favourite a shows see: How do I favourite a podcast or station?
To turn on/off your notifications see: How do I manage notifications in the LiSTNR app?