The update ditches the old tape deck inspired design for a simpler design that features podcast art instead. Overall, the design has been simplified, and there are a couple of new features as well. There is a new option to create custom stations where podcasts will automatically be updated. Stations backup to iCloud and sync to all of your devices. There is also an option for on-the-go playlists, and syncing playlists from iTunes.
Of course, the iOS Podcasts app is one of the worst rated Apple apps available, and there's no guarantee that this update fixes the worst of the issues. There are bug fixes, and the generic performance updates to look forward to. If you want to give it a shot, the Podcasts app is available for free in the iTunes App Store.