Following a show is an option that allows you to reach out all the latest episode of a show you like from the My List section in your app:
Here you can select which followed show you want to browse into by clicking on the the show's rounded picture on the top ( Here Breakfast with Jordan & Perri )
To Follow a show, you will need to go on the show's page of your choice, once there you can see a Follow button just under the show's picture:
By clicking on the follow button, the show will automatically be send to My List where you can find all of the show's latest episode.