A Podcast is a series of audio, video or document files that can be automatically downloaded to a reader or player.
You can pick from many different apps that are designed to play podcasts choose from computer based programs to apps for your phone. Try searching for podcast app or Podcast manager
Once you have your program installed, you can click the Podcast link or copy the link address that is in the text box and paste in to your program. Most programs give you many options on how to handle the updates and downloads.