Blog directory sites are basically directories for website categories, similar to EzineArticles but for blogs instead of articles. This is not the same thing as say a site roll, which is nothing more than a list of blogs one person in particular reads. Often you'll find site rolls on the right hand side of a blog and it will contain the title of the site in question as well as the latest post by that author.
Blog listing sites usually require that you leave a small rectangle on your site with a piece of code which allows them to track your website. This will help them when they show people using their site and searching through a category to find your blog.
To find a directory site, simply Google 'blog listing sites' and look around at what you find. Pick a free website that requires you to put a small bit of code for tracking onto your site and you're ready to go. Add the tracking software somewhere out of sight (I use the very bottom of my website for this purpose) and you will now hopefully start getting more visitors from the listing site you signed up with.
Don't stop at just one site though, be sure to get on as many as you can to improve your readership!
Getting on blog rolls is a great way to get readership, but if you want fresh new visitors who perhaps haven't even heard of your blog yet then you want to get on these blog listing sites. Remember, you can never get enough of this free traffic!