This is a plugin developed by Pat Flynn from SmartPassiveIncome, which arose from a need for a better and more feature-rich podcast player.
It has since evolved into a player, episode list player (with great options) and a bunch of other features like social sharing, fast episode play, download etc.
Not only does this plugin come with all the podcast player features you could wish for, it also looks great with a modern flat design and the ability (pro version) to customize to your branding.
If you are a serious podcaster, I would certainly check this one out as it will take your podcast playback to the next level.
One of the most popular podcasting plugins for WordPress, I have also used this to run my podcast on Mad Lemmings.
It is relatively easy to set up, although I would personally follow a tutorial to make sure you get it right. This is why, although I have not yet tried it, the Serious Simple Podcasting plugin looks simpler and in many ways more powerful. Check that out too.
The main power of such a plugin is getting your RSS feed set up so you can pass that (ie inform) to places like iTunes and Stitcher.
The plugin also gives you a panel to fill in on each post that enables you to hook in your media file (from Libsyn, Soundcloud etc) and turn your blog post into a podcast episode.
They also give you a shortcode to add to your page to position a podcast player, which is actually pretty good. Although there is a better player around developed by Pat Flynn if you can get hold of it.
Not the most well known Podcasting plugin around, but certainly one with enough features to get your attention.
Seriously simple podcasting can help you turn your WordPress website into a podcasting machine by helping you create your iTunes RSS feed (key to getting listeners) , separating your podcasts from your other content by creating specific post types and allowing you to display them separately too.
It also comes with a built in podcast player built on top of the WordPress audio player, which means it is quite robust.
So if you are considering starting a podcast, I would investigate this plugin as your one stop shop to getting up and running.