From then on, you can simply ask Alexa to play a certain show, and you'll be able to continue listening from where you left off on another device. Alexa can fast forward through an episode or skip to the next one. You can also set Apple Podcasts as your default podcast service on Alexa. That way, Alexa will prioritize playback from Apple Podcasts, as long as the show you're asking for is available there.
Apple has one of the biggest podcast services around, so many Alexa users are likely to welcome this news. The cross-device continued listening feature should prove pretty useful.