Guest blogging is a situation when a writer writes the content for a blog that is not their own. That is, you write some good and interesting content, but instead of posting it into your own blog, you give it away to another person to publish in their own blog and specify the original authorship.
Guest blogging is a way to share your expertise and establish yourself as an authority in some field. By creating a guest blog, you expose yourself to a new audience. This is not an advertisement post, but some real content that audience will appreciate.