Get the (purple icon) Podcasts app from the App Store. You'll download from the iTunes app but listen in Podcasts.
Search for a podcast on a topic that interests you. I typed in #edchat. Note that some results are NSFW.
Now this subscription is in my Podcasts app and I can open it anytime and listen.
The blue bubbles indicate which episodes are 'new' for me that I haven't listened to yet.
I hope you find lots of interesting and educational podcasts to enjoy!