It's anonymous bulk text posting - great for sharing logs, but don't discount the more grey side of the internet. If you browse recent public posts there's often some fun things like scam links, credentials, etc.
It's definitely fallen out of favor for password dumps though.
It's useful for sharing configuration files or lengthy error logs etc. when trying to troubleshoot a technical problem with others via chat. AFAIK the original pastebins where invented for such purposes on IRC.