WordPress.org says:
“Permalinks are the permanent URLs to your individual weblog posts, as well as categories and other lists of weblog postings. A permalink is what another weblogger will use to link to your article (or section), or how you might send a link to your story in an e-mail message. The URL to each post should be permanent, and never change — hence permalink.”
The standard permalinks created by WordPress are not very friendly. They look like this – http://yoursite.com/?p=34.
Custom Permalinks settings make your permalinks look like this – http://yoursite.com/postname.
This makes your site more friendly both for human readers and search engine robots.