New is a status for an episode which is set when an episode appears in a podcast.
New episodes are listed in episodes screen and new tab so you can decide to download and add them to your queue.
You can remove the new flag if you don’t want to download an episode and clean up new list. If you do that the episode will be marked as unplayed.
As counter can be set to be either new+unplayed, new or unplayed then I guess even though new episodes are unplayed they do not count when using only unplayed for counter.
Getting back to new flag in my case what I do upon refreshing my podcast is checking all new episodes, decide which ones I want to add to download (which add them to my queue) and then remove all new flag.
If later on I am catch up with episodes in my queue I eventually go to subscriptions, choose some podcast with unplayed episodes and add some to my queue.