A slug is a string of alphanumeric characters (and some special characters) that identify your podcast in a human-readable form. You can think of one as a username for your podcast.
Each podcast uses a slug. This slug is used in URLs, including the URL for your podcast's RSS feed.
For example, if you choose the slug "my-great-podcast", you will have the following URLs:
Changing your slug
The slug of your podcast may be changed, though this may have unintended consequences. If you change your podcast's slug, the URL of the podcast's RSS feed will change. If you have published the RSS feed in a podcast directory like iTunes, you will lose all of your subscribers. Additionally, once your slug has changed, it is now free to be taken by another podcast. If another podcast takes your slug, that podcast will "inherit" the subscribers that previously were subscribed to your podcast, since their new feed URL is the same as your old feed URL.
To change your podcast's slug, please contact support.