To get back links from another relevant blog and traffic of that blog.
Writing for other blogs, allowing guest posts on your own blog build relationships with others in your industry.
Increase Networking.
Guest post increase blog quality. Different authors mean different topics, different perspectives, and different writing styles.
Introduce you to new community.
Writer and owner of blog both promote blog & blog post on their networks.
It improves your blogging skill.
Guest posting generate best quality content.
Search engine also give preference to your blog when many relevant blog recommend your blog content.