First off, wikipedia gives a good explanation of a blog carnival. You can search for carnivals online and submit your blog articles to them. Then, if your article is accepted, you’ll get a link in the carnival back to your blog.
Why should you write for blog carnivals? First off, traffic. Blog carnivals, since they provide a link back to your blog, can generate traffic for you in the short term.
In the long term, people who like reading the article you submitted may also like your blog in general. A handful of people will stick around and become regular readers. Presumably you’re blogging to be read, so more readers is a good thing, right?
Finally, if you’re blogging, you’re probably interested in contributing something to the online discussion in general, and to your topic(s) in particular. You want to be read, and you want to put something useful out there for your readers. Blog carnivals can help you do that.
You can also host a carnival on your site, where you’ll post links to relevant articles on others blogs. This will give you a chance to get to know some other bloggers in your field and perhaps exchange links with them as well.
See this site, for a list of carnivals and their submission guidelines.