Removing downloaded episodes from your Podcasts app can help clear up storage space on your device. You can check your current storage situation by navigating to Settings > General > iPhone Storage. From here you can see how much storage the Podcasts app is using.
You can delete individual episodes in your Podcasts app by navigating to Library > Shows and selecting a show. From here you can scroll through all the listed episodes for the selected show and search for the ones you want to delete. Shows with no iCloud icon are stored on your device. Removing these will help free up storage space.
You can delete a show from your library by lightly pressing and holding down on the show that you want to remove. Tap the "Remove..." tab with the trashcan icon to delete that show from your Podcasts app. You can also delete the shows with iCloud icons from your library the same way.