As the others have already pointed out, it’s a free and easy way to get content, but there’s more.
Big sites often run the risk of growing stale as they uphold their brand. Free guest posts are one way for them to shake things up and allow for some fresh ideas and perspectives, without the danger of compromising the brand they worked so hard on. After all, it’s someone else’s post, right?
While not every writer has a large pool of readers, most do have some audience, and those people will read their guest post. That means a steady trickle of new visitors to the site, many of which may decide to check out the rest of the site’s content.
There’s also the benefit of backlinks and networking. Staying connected is never a bad thing, so the site and the guest poster will essentially help each other with ranking.
Of course, allowing free guest posts does mean that the site will need an active quality control division. Bad content is always worse than insufficient or no content.