It uses the same mechanics as the Android app that came out last year, and syncs across multiple devices if you're signed in to your Google account. The app isn't out on iOS, but you can still use the features on an Apple device's web browser, as highlighted by 9to5Google.
The functionality works across both desktop and mobile. It's especially useful on iOS where a dedicated Google Podcasts app is yet to be released, as 9to5Google notes.
Zack Reneau-Wedeen, Google Podcasts' head of product, tweeted a demonstration of the new functionality on Thursday.
In March, the BBC removed its podcasts from Google's app after concluding that the search giant's policy of directing people looking for BBC podcasts to its own app "reduces people's choice."
First published at 5:19 a.m. PT.
Updated at 5:50 a.m. PT: Adds more detail.