A permalink is a specific URL address that most often goes to blog posts or forum posts after the post has disappeared from the main page. Most modern blogging systems support permalinks (e.g. WordPress). Permalinks are also usually easy for people to read and remember, with the URL usually taking the form of the post title itself, rather than generated characters.
Permalinks (or permanently working links) are desirable in cases where they will be referenced or cited, and it is important that they don't disappear over time. Permalinks are also significantly less susceptible to broken links, which does happen occasionally. In 2003, an experiment found that one out of every 200 links disappeared each week.
Since the content of the Internet was previously static, all links were permalinks. As the web became dynamic, this was less and less true, and many links became broken. The use of permalinks only became significantly more widespread after 2000.